Eccentricity In Exercises 69 and 70, let represent the distance from a focus to the
Chapter 10, Problem 69(choose chapter or problem)
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 an ellipse can be written as \(e=\frac{r_{1}-r_{0}}{r_{1}+r_{0}}\). Then show that \(\frac{r_{1}}{r_{0}}=\frac{1+e}{1-e}\).
Text Transcription:
r_0
r_1
e = r_1 - r_0 / r_1 + r_0
r_1 / r_0 = 1 + e / 1 - e
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