Find the surface area of that part of the plane 9x 5y z=5 that lies inside the elliptic cylinder x216 y281=1

I assume the equation of the plane is and the cylinder has equation .

I don't know what techniques are available to you, so I'll resort to (in my opinion) the most reliable: surface integration.

The surface of intersection is an ellipse in three dimensional space which can be parameterized by , with and .

The area is then given by the integral