Solved: Eccentricity In Exercises 69 and 70, let represent the distance from a focus to

Chapter 10, Problem 70

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In Exercises 69 and 70, let  \(r_{0}\)  represent the distance from a focus to the nearest vertex, and let  \(r_{1}\)  represent the distance from the focus to the farthest vertex.

Show that the eccentricity of a hyperbola can be written as  \(e=\frac{r_{1}+r_{0}}{r_{1}-r_{0}}\). Then show that  \(\frac{r_{1}}{r_{0}}=\frac{e+1}{e-1}\).

Text Transcription:

r_0

r_1

e = r_1 + r_0 / r_1 - r_0

r_1 / r_0 = e + 1 / e - 1

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