Chapter 13.7, Problem 34ES

Show that the equation of the plane that is tangent to the paraboloid

$z=\frac{x^2}{a^2}+\frac{y^2}{b^2}$

at $\left(x_{0,}{y}_0,z_0\right)$ can be written in the from

$z+z_0=\frac{2x_{0}x}{a^2}+\frac{2y_{0}y}{b^2}$