This is how the book describes the problem: If the ellipse x2/a2+y2/b2=1 is to enclose the circle x2+y2=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: x2+(y-1)2=1. I isolated the x2 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/a2+y2/b2=1 but it got messy.