Find the points on the graph of z = x^2e^y at which the tangent plane is parallel to
5x-2y 1/2z=0.

You have a typo in your problem.

What is 5x-2y 1/2z?

+? -?

Are you sure that is not z=x^{2}+e^{y}?

Please make sure the problem is typed exactly as presented.

I doubt if you respond back anyway (few do), but I thought I would mention it in the event you still need help.