Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 692: 10

Elliptic paraboloid

The equation $$4z=9x^2+5y^2$$ can be rewritten as follows $$ z=\left(\frac{x}{2/3}\right)^{2}+\left(\frac{y}{1/\sqrt{3}}\right)^{2} $$ which is an equation of an elliptic paraboloid with $ a=2/3, b=1/\sqrt{3}$ (see equations on page 691).