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If the ellipse x^{2}/a^{2}+y^{2}/b^{2}=1 is to enclose the circle x^{2}+y^{2}=2y, what values of a and b minimize the are of the ellipse?

First of all I completed the square for the second equation and I got: x^{2}+(y-1)^{2}=1. I isolated the x^{2}and substituted it into the ellipse formula because after drawing some diagrams, I realized that if b>a, for a minimal area the ellipse will touch the circle at two points. If a>b, then b=y of the circle.

I'm really lost though... i don't know what to do from here. I don't even know where to start.

I tried solving (y-1)^{2}/a^{2}+y^{2}/b^{2}=1 but it got messy.

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# Homework Help: Optimization - minimize area of an ellipse enclosing a circle

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