Exercise 53

Show that the equation of the tangent plane to the elliptic paraboloid \(z/c = x^2/a^2 + y^2/b^2\) at the point \((x_0, y_0, z_0)\) can be written as \(\frac{2xx_0}{a^2} + \frac{2yy_0}{b^2} = \frac{z + z_0}{c}\)