Start with two circles centered at the origin with radii 0 < a < b (see figure).

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Start with two circles centered at the origin with radii 0 < a < b (see figure). Assume the line ℓ through the origin intersects the smaller circle at Q and the larger circle at R. Let P(x, y) have the y-coordinate of Q and the x-coordinate of R. Show that the set of points P(x, y) generated in this way for all lines ℓ through the origin is an ellipse.

УА R х

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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