standard_description: (+)Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
problem_activity: Problem 1
All the circles below have congruent radii, but different centers.
What polygons can you create from the marked points in the following figure?
Describe the features of each polygon, and use the properties of circles to justify your reasoning.
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Problem 2
Margi has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her calico cat? Use the scale drawing of Margie’s room shown below, together with (only) a compass and straight edge. Place an M where Mack will be if the theory is true.
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Problem 3
The cats changed positions. Mack left the room. Simon and JoJo also moved but stayed the same distance apart. Draw two new locations for Simon and JoJo.
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aligns: no