Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 692: 23

Elliptic paraboloid with the equation $$ y= \left(\frac{x}{2}\right)^{2}+\left(\frac{z}{4}\right)^{2}.$$

The equation of the new surface after the rotation about the $ x $ axis by $90^o $ will be an elliptic paraboloid with the equation $$ y= \left(\frac{x}{2}\right)^{2}+\left(\frac{z}{4}\right)^{2}.$$