1. The problem statement, all variables and given/known data
Consider the ellipsoid 4x^2+2y^2+z^2 = 19. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 2y−8x+z = 0.
3. The attempt at a solution
So I found the normal vector to the tangent, <8x,4y,2z>.
I also found the normal vector to the plane, <-8,2,1>
So what step do I do next? I'm Confused on where to go after this.