55. Confocal Hyperbolas Hyperbolas are called confocal if they have the same foci. (a) Show that the hyperbolas 0

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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55. Confocal Hyperbolas Hyperbolas are called confocal if they
have the same foci.
(a) Show that the hyperbolas
0<k< 16
k
k 16 - k
are confocal.
| (b) Use a graphing device to draw the top branches of
the family of hyperbolas in part (a) for k = 1, 4, 8,
and 12. How does the shape of the graph change as
k increases?
Transcribed Image Text:55. Confocal Hyperbolas Hyperbolas are called confocal if they have the same foci. (a) Show that the hyperbolas 0<k< 16 k k 16 - k are confocal. | (b) Use a graphing device to draw the top branches of the family of hyperbolas in part (a) for k = 1, 4, 8, and 12. How does the shape of the graph change as k increases?
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