The question: Find the maximum distance from the origin to the ellipse .

My work: I figure that the distance to the origin is defined by the equation so that is the function I need to maximize subject to the constraint defined by the equation of the ellipse.

So I've formed the Lagrangian and taken the partials:

After setting all the partials equal to zero, I don't know where to go. No obvious algebraic solutions are coming to mind.