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A Family of Confocal Conics that share a focus are called confocal. Consider the family  of conics that have a focus at 10, 12 and a vertex at the origin, as shown in the figure. a. Find equations of two different ellipses that have these properties. b. Find equations of two different hyperbolas that have these properties. c. Explain why only one parabola satisfies these properties. Find its equation.

A Family of Confocal Conics that share a focus are called confocal. Consider the family  of conics that have a focus at 10, 12 and a vertex at the origin, as shown in the figure. a. Find equations of two different ellipses that have these properties. b. Find equations of two different hyperbolas that have these properties. c. Explain why only one parabola satisfies these properties. Find its equation.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A Family of Confocal Conics that share a focus are called confocal. Consider the family 
of conics that have a focus at 10, 12 and a vertex at the origin, as shown in the figure.
a. Find equations of two different ellipses that have these properties.
b. Find equations of two different hyperbolas that have these properties.
c. Explain why only one parabola satisfies these properties. Find its equation.
d. Sketch the conics you found in parts (a), (b), and (c) on the same coordinate axes 
(for the hyperbolas, sketch the top branches only).
e. How are the ellipses and hyperbolas related to the parabola?

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