calculus and analysis – Backing into point with known equation of plane to known surface equation

All,

I am struggling with writing any code at all to help me solve the following problem.

I have a known function, say $f(x,y) = xy^2.$

I also know the equation of a plane tangent to the point P of this surface, say $x + 6y -6$.

I want to find the point P. Any suggestions about how to do this? Thanks so much.