Chapter 14.6, Problem 51E

Show that the equation of the tangent plane to the ellipsoid x²/a² + y²/b² + z²/c² = 1 at the point (x₀, y₀, z₀) can be written as

$\frac{x{x}_0}{a^2}+\frac{y{y}_0}{b^2}+\frac{z{z}_0}{c^2}=1$