Thread: Finding all points on the surface parallel to a plane

"Consider the surface given by 4x^2-y^2+5z^2-10z=55.

a) Find all points on the surface at which the tangent plane is parallel to the plane 8x+y+15z=1.
b) Pick one of these points and give the equation of the tangent plane to the surface at that point."

My work so far:

I'm stuck on this one. Part B is easy enough once you figure out part A, but I'm not sure what to do after a certain point.

g(x,y,z)= 8x, -2y, 10z-10

So what I'm looking for is a value of k such that 8x, -2y, 10z-10 = k (8,1,15).

But I don't know how to find k. Any help would be appreciated.

The point with must satisfy the equation of the surface.