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$$x^2=4y-2y^2$$

I figured out it was an ellipse but I don't know where to go next. I don't know how to modify it to where it fulfills the form of an ellipse. Please help.

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1 Answer

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$$\begin{align} x^2=4y-2y^2&\iff x^2+2y^2-4y=0\\ &\iff x^2+ 2(y^2-2y)=0\\ &\iff x^2+2(y^2-2y+1)=2\\ &\iff x^2+2(y-1)^2=2\\ &\iff \frac{x^2}{2}+\frac{(y-1)^2}{1}=1. \end{align}$$ Can you now find the vertices, and foci?

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