?A point on an ellipse with major axis length 2a and minor axis length 2b has the
Chapter 5, Problem 203(choose chapter or problem)
A point on an ellipse with major axis length 2a and minor axis length 2b has the coordinates \((a \cos \theta, b \sin \theta)\), \(0 \leq \theta \leq 2 \pi\).
(a) Show that the distance from this point to the focus at (-c, 0) is \(d(\theta)=a+c \cos \theta\), where \(c=\sqrt{a^{2}-b^{2}}\)
(b) Use these coordinates to show that the average distance \(\bar{d}\) from a point on the ellipse to the focus at (-c, 0), with respect to angle \(\theta\), is a.
Text Transcription:
(a cos theta, b sin theta)
0 leq theta leq 2 pi
d(theta)=a+c cos theta
c=sqrt a^2-b^2
bar d
theta
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