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Find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12.

How many pairs of positive integers $(x,y)$ are there which lie below the graph of the hyperbola $xy = 16$?

The figure below shows the ellipse $\frac{(x-20)^2}{20}+\frac{(y-16)^2}{16}=2016$. [asy] defaultpen(linewidth(0.7)); pair c=(20,16); real dist = 30; real a = sqrt(2016*20),b=sqrt(2016*16); xaxis("x",c.x-a-dist,c.x+a+3*dist,EndArrow); yaxis("y",c.y-b-dist*...

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