Solved: Conjecture (a) Show that the equation of an ellipse can be written as (b) Use a
Chapter 10, Problem 82(choose chapter or problem)
(a) Show that the equation of an ellipse can be written as
\(\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{a^{2}\left(1-e^{2}\right)}=1\).
(b) Use a graphing utility to graph the ellipse
\(\frac{(x-2)^{2}}{4}+\frac{(y-3)^{2}}{4\left(1-e^{2}\right)}=1\)
for e = 0. 95, e = 0. 75, e = 0. 5, e = 0. 25, and e = 0.
(c) Use the results of part (b) to make a conjecture about the change in the shape of the ellipse as \(e\) approaches 0.
Text Transcription:
(x - h)^2 / a^2 + (y - k)^2 / a^2 (1 - e^2) = 1
(x - 2)^2 / 4 + (y - 3)^2 / 4(1 - e^2) = 1
e
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