Two solids, $x^2+y^2+z^2=8$ and $z^2=x^2+y^2$ go through the point $P$: $(2,0,2)$.
My task is to determine an equation for the tangentline to the intersection curve of the two solids at the point $P$.
My first thought was that the intersection curve must be perpendicular to the two solids, and then somehow figuring out the derivative of the curve in some way. But I'm not sure how.
HINT:
Find the normal vectors to both surfaces at the point $P$. Then the tangent vector is just the cross product of those two vectors. Then you should be able to find the tangent line.