Question

Show that r(t) = a parameterization for an ellipse by showing that x(t) and y(t) satisfy x^2/a^2 + y^2/b^2 = 1 for some a and b.

Answer 1

representing x and y separately we have\[x=\sin t\]\[y=2\cos t\to \frac y2=\cos t\]and using the trig identity we get\[\sin^2 t+\cos^2t=1\]\[\frac{x^2}1+\frac{y^2}4=1\]which is an ellipse

Answer 2

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Answer 3

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Answer 4

I'm sorry I'm going to sleep...