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May 10th, 2017, 02:41 AM   #1
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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?
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May 10th, 2017, 04:33 AM   #2
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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.
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