



 
Firstly, if you plot the "ellipse" you will see that it is a rather special ellipse, usually given another name. Now there are two ways to proceed. The traditional way is to solve for one variable, say find y as a function of x. Then find the area as a function of $x: A(x) = x \times y(x),$ take its derivative, and set equal to 0. You can also differentiate the constraint equation implicitly: $x/2 + (y/2) y' = 0$ Good Hunting!  


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