Question

Find the points on the graph of z=(3x^2)-(4y^2) at which the vector n = <3,2,2> is normal to the tangent plane.

Answer 1

\[ z=(3x^2)-(4y^2) \\
\phi (x, y, z) = 3x^2 - 4y^2 - z \\
\nabla \phi = <3,2,2>\]
solve for x,y,z