I'm trying to find the cartesian equation of the curve which is defined parametrically by:
$$ x = 2\sin\theta, y = \cos^2\theta $$
Both approaches I take result in the same answer:
$$ y = 1 - \sin^2\theta\\ \sin \theta = \sqrt{y-1} \\ x = 2\sqrt{y-1} \\ x^2 = 4(y- 1) \\ x^2 + 4 = 4y $$ Method 2: $$ \sin^2 = y - 1 \\ \sin\theta = \frac{x}{2} \\ \sin^2\theta = \frac{x^2}{4} \\ x^2 + 4 = 4y $$
But the answer listed is $x^2 + 4y^2 = 4$. Are my calculations wrong?