(723, #41) Find an equation for the surface obtained by rotating the parabola about the y-axis.

Solution: The surface of rotation is a paraboloid with its major axis along the y-axis.

The vertex of the paraboloid is at the origin. The trace for the surface on the yz-plane is also a parabola, with the equation at x = 0.

Thus the equation of the surface obtained by rotating the parabola about the y-axis is

Maple code

by: gm