Assertion: ellipse | /r/HasProperty | the set of all points
Facets:
value: in a plane
type: LOCATION
value: in effect
type: OTHER
value: from a pre-calculus perspective
type: OTHER
Source sentences:
text: An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant.
text: If you would analyze analytically then Ellipse is a set of points that is defined as the ratio of the distance from any particular point to the curve whose sum is a constant number.
text: An ellipse is the set of points in a plane such that the sum of the distances from two fixed points in that plane stays constant.
text: Equivalently, it is defined as the locus, or set, of all points such that the sum of the distances from to two fixed foci is a constant.
text: An ellipse if we speak in terms of locus, it is the set of all points on a XY-plane, whose distance from two fixed points (known as foci) adds up to a constant value.
text: Ellipse is the set of all points on a plane whose distance from two points add up to a constant.
text: An ellipse is the set of all points ( x , y ) ( x , y ) in a plane such that the sum of their distances from two fixed points is a constant.
text: An ellipse is the set of all points ( x , y )
text: The ellipse is the set of all points ( x , y )
text: An ellipse is the set of all points ( x , y ) in a plane such that the sum of their distances from two fixed points is a constant.
text: An ellipse is the set of all points in the plane the sum of whose distances from two fixed points, called the foci, is a constant.
text: An ellipse is the set of all points P such that the sum of the distances between P and two distinct points, called the foci (±c, 0), is a constant.
text: An ellipse is the set of all points \((x,y)\) in a plane such that the sum of their distances from two fixed points is a constant.
text: The ellipse is the set of all points \((x,y)\)
text: An ellipse is the set of all points in a plane such that the sum of the distances from two fixed points (foci) is constant.
text: An ellipse is the set of all points in a plane the sum of whose distances from two ﬁxed points is constant.
text: In defining an ellipse, we fix two points, called the foci, and then define the ellipse to be the set of all points such the sum of the distances from those foci is a given constant.
text: An ellipse is the set of all points which are a constant sum of the distance from two foci.
text: Ellipse is a set of points where two focal points together are named as Foci and with the help of those points, Ellipse can be defined.
text: An ellipse is a set of points on a plane, creating an oval, curved shape, such that the sum of the distances from any point on the curve to two fixed points (the foci) is a constant (always the same).
text: An ellipse is a set of points, the sum of whose distances from two fixed points (the foci, which lie on the major axis) is constant.
text: An ellipse is a set of points whose distances from a fixed point (the focus) and fixed line (the directrix) are in a constant ratio less than 1.
text: An ellipse is a set of points (x, y) in a Cartesian plane satisfying an equation of the form x2/a2 + y2/b2 = 1, where a is the distance from the origin to the end of the x axis on the ellipse (semimajor axis), b is the distance from the origin to the end of the y axis on the ellipse (semiminor axis), and a >
text: An ellipse is a set of points (x, y) in a Cartesian plane satisfying the parametric equations x = a cos t and y = b sin t, where a and bare constants and
text: From a pre-calculus perspective, an ellipse is a set of points on a plane, creating an oval, curved shape such that the sum of the distances from any point on the curve to two fixed points (the foci) is a constant (always the same).
text: An ellipse is the affine image of a circle; an ellipse is a non-degenerate conic (i.e. a second-order curve) which does not meet the line at infinity; an ellipse is the set of points whose distances to a given point (the focus) and to a given line (the associated directrix) are in constant ratio; and an ellipse is a planar compact non-singular algebraic curve of the second degree.
text: An ellipse is the set of points in a plane whose distance from
text: In effect, then, if we call the foci $F_1,F_2$ and arbitrary points $P$, and call our given constant $c$, then the ellipse is the set of points $P$ such that