Find the area of the largest rectangle that can be inscribed in the ellipse
$\displaystyle x^2 / a^2 + y^2 / b^2 = 1$
All I have so far is that the area = 4xy
Not sure where to go next; too many variables.
Since the corners of the rectangle are on the ellipse, the "x" and "y" in xy must satisfy $\displaystyle x^2/a^2+ y^2/b^2= 1$. As Unknown008 said, a and b are constants not variables. You can either write $\displaystyle y= b\sqrt{1- x^2/a^2}$ or differentiate xy with respect to x: y+ xy'= 0, and get y' by differentiating $\displaystyle x^2/a^2+ y^2/b^2= 1$ implicitely.