Any experienced calculus students here? I would appreciate some help with this problem.

Find an equation for a family of orthogonal curves to this curve and show me every step that you took

x^2 + 2y^2 = k^2

As far as I understand, you have to get y by itself, derive it, take the negative inverse of the derivative, then integrate it. I'm not getting the right answer though...

This might help

Ah. Partial derivatives. That helped a lot. Thank you