Find an equation for the surface obtained by rotating the parabola
y = x^2
about the y-axis.

## Answer

Selutioa: The serace ef rotatiea is a parakobid with ies major axis along the y-sis ne vertex of the parabelid is al the erigia. The trace for the surface oa the yapise is alse parabola, with the eqution y-z” at x . 0. Thes the equatione of the sarface obeained by retatig he parabola yx abost the y-axis i

Selutioa: The serace ef rotatiea is a parakobid with ies major axis along the y-sis ne vertex of the parabekid is al the erigia. The trace for the surface oa the yaplane is alse parabola, with the eqution y-z” at x . 0. Thes the equation of the sarface olesind by retng te parabola y sbot dhe y asis i

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 y=z^2 at x = 0.

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

y=x^2 about the axis

y=x^2+z^2