<PAGE>   1
                                                                    EXHIBIT 10.7

                               SECURITY AGREEMENT


     THIS SECURITY AGREEMENT (the "Agreement") is entered into as of the 29th
day of September, 2000, by and between Liberty PL2, Inc. (the "Debtor"), and
Liberty Media Corporation (the "Secured Party").

                                    RECITALS

     The Secured Party has advanced to the Debtor the principal sum of U.S.
$123,943,050 pursuant to the terms of an Amended and Restated Promissory Note of
even date herewith (the "Note") executed by the Debtor as maker in favor of the
Secured Party as payee. To secure the prompt payment of the indebtedness
evidenced by the Note, the Debtor wishes to assign to the Secured Party all
rights, title and interests in the Debtor's ownership interest in Liberty PL3,
LLC, a Delaware limited liability company (the "Company"), as governed by that
certain First Amended and Restated Operating Agreement dated as of September 29,
2000, to which Debtor is a party, as the same may be amended from time to time
(the "Operating Agreement").

     In consideration of the mutual promises and covenants contained in this
Agreement and intending to be legally bound, the Debtor and the Secured Party
agree as follows:

                                    AGREEMENT

     1. Definitions. The following terms, when used in this Agreement, have the
meanings set forth below:

          "Bankruptcy" means, as to the Debtor, the occurrence of any of the
following:

          (a) the making by such Person of a general assignment for the benefit
of creditors;

          (b) the filing by such Person of a voluntary petition in bankruptcy;

          (c) the adjudication of such Person as bankrupt or insolvent, or the
entry of an order, judgment or decree by any court of competent jurisdiction,
granting relief against such Person in any bankruptcy or insolvency proceeding;

          (d) the filing by such Person of a petition or answer seeking for such
Person any reorganization, arrangement, composition, readjustment, liquidation,
dissolution or similar relief under any statute, law or regulation;

          (e) the filing by such Person of an answer or other pleading admitting
or failing to contest the material allegations of a petition filed against such
Person in any proceeding for reorganization, arrangement, composition,
readjustment, liquidation, dissolution or similar proceeding under any statute,
law or regulation;



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          (f) the valid appointment, with the consent of such Person, of a
receiver, trustee or liquidator to administer all or a substantial portion of
such Person's assets or, in the case of the Debtor, the Ownership Interest; or

          (g) the valid appointment, without the consent of such Person, of a
receiver, trustee or liquidator to administer all or a substantial portion of
such Person's assets or, in the case of the Debtor, the Ownership Interest, if
such appointment is not vacated or stayed within 90 days after such appointment
or, if stayed, such appointment is not vacated within 90 days after such stay.

          "Business Day" means any day other than Saturday, Sunday or a day on
which banking institutions in Denver, Colorado, are required or authorized to be
closed.

          "Company" shall have the meaning specified in the Recitals.

          "Debtor" shall have the meaning specified in the preamble.

          "Distribution" means any distribution of cash or other property by the
Company with respect to the Ownership Interest, including without limitation,
all operating and liquidating distributions.

          "Event of Default" shall have the meaning specified in Section 8.

          "Lien" means a mortgage, lien, pledge, security interest or other
encumbrance.

          "Note" shall have the meaning specified in the Recitals.

          "Operating Agreement" shall have the meaning specified in the
Recitals.

          "Ownership Interest" means all of the interests of the Debtor in the
Company, whether now owned or hereafter acquired, including all rights of the
Debtor under the Operating Agreement.

          "Person" means a human being or a corporation, partnership, limited
liability company, trust, unincorporated organization, association or other
entity.

          "Secured Obligations" shall have the meaning specified in Section 2.

          "Secured Party" shall have the meaning specified in the preamble.


     2. Grant of Security Interest. As security for (a) the timely fulfillment
and performance of each and every covenant and obligation of the Debtor under
this Agreement, and (b) the payment of all obligations owed to the Secured Party
under this Agreement and the Note, as it may be amended from time to time, and
any and all damage which the Secured Party may suffer by reason of a breach by
the Debtor of any obligation, covenant or undertaking with respect to this
Agreement,

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the Note or any extensions, renewals or amendments of either of the foregoing,
to the Secured Party, however created, acquired, arising or evidenced, whether
direct or indirect, absolute or contingent, now or hereafter existing, or due or
to become due (all of the foregoing obligations of (b) being hereinafter
collectively referred to as the "Secured Obligations"), the Debtor hereby
pledges, mortgages, transfers, sets over and delivers to and assigns to the
Secured Party and grants the Secured Party a continuing Lien and security
interest in and to:

          (i) the Ownership Interest. Without limiting the generality of the
foregoing, Secured Party is hereby granted a security interest in the Ownership
Interest and all of Debtor's rights, title and interests therein, including all
rights of Debtor to receive any and all Distributions; and

          (ii) all proceeds of, and substitutions for, any and all of the
foregoing; in each case, whether now owned or hereafter acquired by the Debtor,
howsoever its interest therein may arise or appear (whether beneficially or of
record and whether by ownership, security interest, claim or otherwise).

     Concurrently with the execution of this Security Agreement, Debtor shall
execute and deliver to Secured Party an "Assignment of Ownership Interest" in
the form attached to this Agreement as Exhibit A. Debtor hereby authorizes
Secured Party, upon the occurrence of an Event of Default and after the
expiration of any applicable cure period therefor, to execute the Assignment of
Ownership Interest. Debtor agrees that the Company and its Members and Manager
(as such terms are defined in the Operating Agreement) shall be entitled to rely
conclusively on such Assignment of Ownership Interest and shall have no
liability to Debtor for any loss or damage which Debtor may incur by reason of
such reliance.

     Nothing in this Agreement shall constitute an assumption by Secured Party
of any liability or obligation of Debtor with respect to the Ownership Interest.
Debtor shall remain liable under the Operating Agreement to perform all of its
obligations thereunder to the same extent as if this Agreement had not been
executed. The exercise of the Secured Party of any of his rights hereunder shall
not release Debtor from any of its obligations under the Operating Agreement.

     All rights of the Debtor to receive any distributions, dividends, stock,
instruments, securities and other distributions shall be vested in the Secured
Party, which shall have the sole and exclusive right and authority to receive
and retain such distributions and dividends. All distributions or dividends
which are received by the Debtor contrary to the provisions of this Section 2
shall be received in trust for the benefit of the Secured Party, shall be
segregated from other property or funds of the Debtor and shall be forthwith
delivered to the Secured Party as Collateral in the same form as so received
(with any necessary endorsement). Any and all money and other property paid over
to or received by the Secured Party pursuant to the provisions of this Section 2
shall be retained by the Secured Party in an account to be established by the
Secured Party upon receipt of such money or other property and shall be applied
in accordance with the provisions of the Note.


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     3. Representations and Warranties. The Debtor hereby represents and
warrants to the Secured Party as follows: (a) except for the security interest
created hereby, the Debtor is and will at all times be the legal and beneficial
owner of the Ownership Interest, free and clear of all Liens, other than the
encumbrances created by the Operating Agreement (as in effect on the date
hereof); (b) the Debtor has the unencumbered right and power to pledge the
Ownership Interest as provided herein; (c) all actions necessary or desirable to
perfect, establish the first priority of, or otherwise protect, the security
interest of the Secured Party in the Ownership Interest have been duly taken;
(d) the exercise by the Secured Party of his rights and remedies hereunder will
not contravene any law or governmental regulation or any contractual restriction
binding on or affecting the Debtor or any of its properties and will not result
in or require the creation of any Lien upon or with respect to any of its
properties, except for restrictions on transfer contained in the Operating
Agreement; (e) no authorization or approval or other action by, and no notice to
or filing with, any court, agency, department, commission, board, bureau or
instrumentality of the United States or any state or other political subdivision
thereof or regulatory body, or any other third party, except as has previously
been obtained, is required either (i) for the grant by the Debtor of the Lien
and security interest created hereby in the Ownership Interest, or (ii) for the
exercise by the Secured Party, of his rights and remedies hereunder, except as
may be required in respect of any such exercise by laws affecting the offering
and sale of securities generally and except as may be required under the terms
of the Operating Agreement; and (f) this Agreement creates a valid Lien and
security interest in favor of the Secured Party in the Ownership Interest, as
security for the Secured Obligations.

     4. No Liens. The Debtor covenants and agrees that it will not: (a) sell or
otherwise dispose of all or any part of the Ownership Interest provided,
however, that the Debtor is permitted to sell its 1% common interest in the
Company to the Secured Party; or (b) create or permit to exist any Lien upon or
with respect to the Ownership Interest, other than the Lien and security
interest created hereunder in favor of the Secured Party.

     5. Covenants. So long as any of the Secured Obligations shall remain
outstanding, the Debtor shall: (a) at its own expense, promptly deliver to the
Secured Party a copy of each notice or other communication received by it in
respect of any of the Ownership Interest; (b) not make or consent to any
amendment or other modification or waiver with respect to the Ownership Interest
which could be adverse to the interests of the Secured Party, or enter into any
agreement or permit to exist any restriction with respect to the Ownership
Interest other than pursuant hereto; or (c) not take any action which would (or
fail to take any action, the result of which failure would) in any manner impair
the value of the Ownership Interest or the priority or enforceability of the
security interest of the Secured Party.


     6. Power of Attorney. Effective upon the occurrence and during the
continuance of an Event of Default, the Debtor hereby irrevocably appoints the
Secured Party as its attorney-in-fact, with full power and authority in the
place and stead of the Debtor and in the name of the Debtor or otherwise, from
time to time in the Secured Party's discretion, to take any action and execute
any documents which the Secured Party may deem necessary or desirable in
connection with the terms and provisions of this Agreement, including, without
limitation, to receive, endorse and collect all instruments made payable to the
Debtor representing any payment on or any Distribution in respect


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of the Ownership Interest or any part thereof and to give full discharge for the
same. If the Debtor fails to perform any agreement or obligation contained
herein, the Secured Party himself may perform, or cause performance of, such
agreement or obligation, and the reasonable expenses that the Secured Party
incurs in connection therewith shall be payable by the Debtor and deemed a part
of the Secured Obligations.

     7. Indemnity and Expenses.


     (A) The Debtor agrees to indemnify the Secured Party from and against any
and all reasonable claims, losses and liabilities growing out of or resulting
from this Agreement (including, without limitation, enforcement of this
Agreement), except claims, losses or liabilities resulting solely and directly
from the gross negligence or willful misconduct of the Secured Party.

     (B) The Debtor will, upon demand, pay to the Secured Party the amount of
any and all reasonable expenses, including the disbursements and reasonable fees
of the Secured Party's counsel and of any experts, consultants and agents, which
the Secured Party may incur in connection with (i) the administration of this
Agreement; (ii) the custody, preservation, use or operation of, or the sale of,
collection from, or other realization upon, the Ownership Interest; (iii) the
exercise or enforcement of any of the rights of the Secured Party hereunder; or
(iv) the failure by the Debtor to perform or observe any of the provisions
hereof.

     8. Event of Default. The occurrence of any of the following shall
constitute an event of default ("Event of Default") hereunder:

     (a) (i) any default in the prompt and complete payment and performance of
the Note; or (ii) any default in the prompt and complete payment and performance
of any term, condition or covenant in favor of Secured Party contained in this
Agreement or in any other agreement or instrument delivered pursuant thereto or
hereto; in each case where such default is not cured within any applicable cure
period which may be granted in the Note or any such agreement or instrument with
respect to such default or, if no specific cure period is granted with respect
to such default, where such default is not cured within ten Business Days after
notice thereof from Secured Party or his successors or assigns;

     (b) the Bankruptcy of the Debtor or the Company;

     (c) the transfer of property by the Debtor or the Company under
circumstances that would entitle a trustee in bankruptcy or similar fiduciary to
avoid such transfer under the federal bankruptcy laws, as amended, or under any
other laws, whether federal or state, for the relief of debtors, now or
hereafter existing;

     (d) the cessation of the Company to be a going concern;

     (e) if any representation made by Debtor to Secured Party hereunder should
prove to be false or misleading;


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     (f) if final judgment for the payment of money in excess of $100,000.00
shall have been rendered by any court of competent jurisdiction against Debtor
or the Company and the same has not been discharged or varied or execution
thereunder stayed, whether pursuant to appeal or otherwise, within 30 days of
the entry thereof, or if any final order, ruling or direction of any competent
authority is issued with respect to Debtor or the Company that materially
adversely affects Debtor or the Company or that requires a substantial or
material adverse change in the business or affairs of the Debtor or the Company
or any material disposition of assets of the Debtor or the Company; or

     (g) if there shall be any materially adverse change in the financial
condition of Debtor or the Company.

     9. Secured Party's Rights Upon Default. In the event of the occurrence and
during the continuance of an Event of Default, the Secured Party may, without
the necessity of foreclosure and as a means of substituting collateral, sell,
transfer or otherwise dispose of the Ownership Interest or any right therein or
any part thereof after ten Business Days' prior written notice to the Debtor, in
one or more parcels, at the same or different times, at a public or private
sale, or may make any other commercially reasonable disposition of the Ownership
Interest or any portion thereof. The Secured Party may purchase the Ownership
Interest or any portion thereof. The proceeds of the sale or other disposition
shall be applied to the Secured Obligations in such order as set forth in the
Note. Any remaining proceeds shall be paid over to the Debtor or others as
provided by law.

     10. Voting Rights. Unless and until an Event of Default shall have occurred
and be continuing, the Debtor shall be entitled to exercise any and all voting
and/or consensual rights and powers accruing to an owner of the Ownership
Interest or any part thereof for any purpose not inconsistent with the terms of
this Agreement and the Note provided that such action would not adversely affect
the rights inuring to the Secured Party under this Agreement or the Note.

     11. Additional Rights of Secured Party. In addition to its rights and
privileges under this Agreement, the Secured Party shall have all the rights,
powers and privileges of a secured party under the Uniform Commercial Code as in
effect in the State of Colorado, and such other rights or remedies which it may
have at law or in equity.

     12. Termination and Release. Upon the payment in full of the Secured
Obligations, the Secured Party shall take any actions reasonably necessary to
terminate and release the security interest in and security title to the
Ownership Interest granted to the Secured Party hereunder, and to cause the
Assignment of Ownership Interest to be returned to the Debtor, all at the cost
and expense of the Debtor.


     13. Disposition of Ownership Interest by the Secured Party. To the extent
that the Ownership Interest is not registered under the various federal or state
securities acts, the disposition thereof after the occurrence and during the
continuance of an Event of Default may be restricted to one or more private
(instead of public) sales in view of the lack of such registration; the Debtor
understands that, upon such disposition, the Secured Party may approach only a
restricted number


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of potential purchasers and further understands that a sale under such
circumstances may yield a lower price for the Ownership Interest than if the
Ownership Interest were registered pursuant to federal and state securities
legislation and sold on the open market. The Ownership Interest is not, as of
the date of this Agreement, registered under the various federal and state
securities laws. The Debtor, therefore, agrees that:

     (A) if the Secured Party, pursuant to the terms of this Agreement, sells or
causes the Ownership Interest or any portion thereof to be sold at a private
sale, the Secured Party shall have the right to rely upon the advice and opinion
of any national brokerage or investment firm having recognized expertise and
experience in connection with shares or obligations of companies or entities in
the same or similar business as the Company which brokerage or investment firm
shall have reviewed financial data and other information available to the
Secured Party pertaining to the Company (but shall not be obligated to seek such
advice and the failure to do so shall not be considered in determining the
commercial reasonableness of the Secured Party's action) as to the best manner
in which to expose the Ownership Interest for sale and as to the best price
reasonably obtainable at the private sale thereof; and

     (B) such reliance shall be conclusive evidence that the Secured Party have
handled such disposition in a commercially reasonable manner.

     14. Debtor's Obligation Absolute.


     (A) The obligations of the Debtor under this Agreement shall be direct and
immediate and not be conditional or contingent upon the pursuit of any other
remedies against any Person, nor against other security or Liens available to
the Secured Party or his successors, assigns or agents. The Debtor waives any
right to require that an action be brought against any other Person or to
require that the Secured Party resort to any security or to any balance of any
deposit account or credit on the books of Secured Party in favor of any other
Person or to require resort to rights or remedies hereunder prior to the
exercise of any other rights or remedies of the Secured Party in connection with
the Secured Obligations.


     (B) The obligations of the Debtor hereunder shall remain in full force and
effect without regard to, and shall not be impaired by: (i) any bankruptcy,
insolvency, reorganization, arrangements, readjustment, composition, liquidation
or the like of the Debtor or any affiliate of the Debtor; (ii) any exercise or
nonexercise, or any waiver, by the Secured Party of any rights, remedy, power or
privilege under or in respect of the Secured Obligations or this Agreement, or
any security for any of the Secured Obligations (other than this Agreement); or
(iii) any amendment to or modification of the Secured Obligations or this
Agreement, or any security for any of the Secured Obligations (other than this
Agreement), whether or not the Debtor shall have notice or knowledge of any of
the foregoing.

     15. Notices. All notices and other communications required or permitted to
be given hereunder shall be in writing and shall be addressed as follows:


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                  If to Secured Party:

                  Liberty Media Corporation
                  9197 South Peoria Street
                  Englewood, CO  80112
                  Attention:  General Counsel

                  If to Debtor:

                  Liberty PL2, Inc.
                  1100 Glendon Avenue
                  Suite 2000
                  Los Angeles,  CA 90024
                  Attention:  General Counsel

Any notice given in accordance with this Section 15 shall be deemed to have been
given (a) on the date of receipt if personally delivered, (b) five days after
being sent by U.S. mail, postage prepaid, (c) the date of receipt, if sent by
registered or certified U.S. mail, postage prepaid, (d) one Business Day after
receipt, if sent by confirmed facsimile or telecopier transmission or (e) one
Business Day after having been sent by a nationally recognized overnight courier
service. In computing time periods, the day of the notice will be included.

     16. Security Interest Absolute. All rights of the Secured Party, and all
security interests and all obligations of the Debtor hereunder shall be absolute
and unconditional irrespective of: (a) any lack of validity or enforceability of
the Note or of any other document executed in connection therewith ; (b) any
change in the time, manner or place of payment of, or any other term in respect
of, all or any of the Secured Obligations, or any other amendment or waiver of
or consent to any departure from the terms of the Note; or (c) any increase in,
addition to, exchange or release of, or non-perfection of any Lien on or
security interest in any other collateral or any release or amendment or waiver
of or consent to departure from any security document or guaranty, for all or
any of the Secured Obligations.

     17. Binding Agreement. The provisions of this Agreement shall be construed
and interpreted, and all rights and obligations of the parties hereto
determined, in accordance with the internal laws of the State of Colorado. This
Agreement, together with all documents referred to herein, constitutes the
entire agreement between the Debtor and the Secured Party with respect to the
subject matter hereof, and may not be modified except by a writing executed by
the Secured Party and the Debtor, and no waiver of any provision of this
Agreement, and no consent to any departure by the Debtor therefrom, shall in any
event be effective unless the same shall be in writing and signed by the Secured
Party, and then such waiver or consent shall be effective only in the specific
instance and for the specific purpose for which given. This Agreement shall be
binding upon the Debtor and its successors and assigns, and shall inure to the
benefit of the Secured Party and his successors and assigns.


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     18. Severability. Whenever possible each provision of this Agreement shall
be interpreted in such manner as to be effective and valid under applicable law,
but if any provision of this Agreement shall be prohibited or invalid under such
law, such provision shall be ineffective only to the extent of such prohibition
or invalidity, without invalidating the remainder of such provision of this
Agreement.

     19. Further Assurances. The Debtor agrees, at its expense, to execute,
acknowledge, deliver and cause to be duly filed all such further instruments and
documents and take all such actions as the Secured Party may from time to time
reasonably request for the assuring and preserving of the security interest
granted hereunder and the rights and remedies created hereby, including, without
limitation, the payment of any fees and taxes required in connection with the
execution and delivery of this Agreement, the granting of the security interest
and the filing of any financing statements or other documents in connection
herewith. If any amount payable under or in connection with any of the
Collateral shall be or become evidenced by any promissory note or other
instrument, such note or instrument shall be promptly pledged and delivered to
the Secured Party, duly endorsed in a manner satisfactory to the Secured Party.
The Debtor agrees to notify promptly the Secured Party of any change in its
corporate name or in the location of its chief executive office, its chief place
of business or the office where it keeps its records relating to the Collateral
and the location of any Collateral. The Debtor agrees promptly to notify the
Secured Party if any material portion of the Collateral is damaged or destroyed.

     20. Miscellaneous. No failure to exercise, and no delay in exercising, any
right hereunder by the Secured Party shall operate as a waiver thereof, nor
shall any single or partial exercise of any such right preclude any other or
future exercise thereof or the exercise of any other right. The rights and
remedies of the Secured Party provided herein are cumulative and are in addition
to, and not exclusive of, any rights or remedies provided by law. The rights and
remedies of the Secured Party hereunder against any party thereto are not
conditional or contingent on any attempt by the Secured Party to exercise any of
his rights under the Note against such party or against any other Person.

     21. Counterparts. This Agreement may be executed in any number of
counterparts, each of which shall be deemed to be an original and all of which,
when taken together, shall constitute one and the same instrument, and each of
the parties hereto may execute this Agreement by signing any such counterpart.



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     IN WITNESS WHEREOF, the undersigned have hereunto set their hands, by and
through their duly authorized signatories, as of the day and year first above
written.

                               DEBTOR:

                               LIBERTY PL2, INC.



                               By:
                                        ----------------------------------------
                               Name:    Mark D. Rozells
                               Title:   Executive Vice President


                               SECURED PARTY:

                               LIBERTY MEDIA CORPORATION



                               By:
                                        ----------------------------------------
                               Name:    Charles Y. Tanabe
                               Title:   Senior Vice President




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                                    EXHIBIT A

                        ASSIGNMENT OF OWNERSHIP INTEREST


     The undersigned TRANSFEROR hereby transfers and assigns its Ownership
Interest in LIBERTY SATELLITE, LLC, a Delaware limited liability company (the
"Company"), to Liberty Media Corporation, as TRANSFEREE. The Capital Account of
the TRANSFEROR that is attributable to the transferred Ownership Interest will
carry over to the TRANSFEREE. The Ownership Interest transferred is subject to
all of the terms and conditions of that certain Operating Agreement of LIBERTY
PL3 LLC, dated September 29, 2000 as such Agreement may be amended ("Operating
Agreement").

                                     TRANSFEROR:

                                     LIBERTY PL2, INC.


                                     By:
------------------------                ----------------------------------------
         Date                        Name:
                                          --------------------------------------
                                     Title:
                                           -------------------------------------




                        ACCEPTANCE OF OWNERSHIP INTEREST

     The undersigned, as TRANSFEREE, accepts the above transfer of an Ownership
Interest in the Company as governed by the Operating Agreement and agrees to be
bound as a party to such Operating Agreement (which, as it may be amended, is
hereby incorporated by reference).



                                     NAME OF TRANSFEREE:

                                     LIBERTY MEDIA CORPORATION


                                     By:
------------------------                ----------------------------------------
         Date                        Name:
                                          --------------------------------------
                                     Title:
                                           -------------------------------------



                                     A-1