1. The problem statement, all variables and given/known data I have a surface given by z=x^2 - y^2 and its tangent plane at the point (x,y)=(1,1) given by z = 2x-2y. I am asked to compute the intersection of the tangent plane with the surface. 3. The attempt at a solution I did the obvious and set x^2-y^2 = 2x -2y to find the x,y lying on their intersection. I moved all of the terms to the RHS and used the quadratic formula to obtain x=y and x+y=2. If x=y, then obviously z=0. I'm a little lost on what to do with the x+y=2. I know what the two graphs look like and I know what their intersection looks like, but I am trying to justify my answer.