My Math Forum ellipse question

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 May 10th, 2017, 01:41 AM #1 Member   Joined: Jan 2016 From: Blackpool Posts: 95 Thanks: 2 ellipse question Let γ : R → R 2 be the plane curve given by γ(t) = (3 tanh t, 2 sech t). Show that the image of γ is contained in an ellipse, and determine the equation of the ellipse. Is the image the whole ellipse?
 May 10th, 2017, 03:33 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,059 Thanks: 1618 As tanh²t + sech²t ≡ 1, an equation for the ellipse is (x/3)^2 + (y/2)^2 = 1. As sech t > 0, the image isn't the whole ellipse. Thanks from Jaket1

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