Find an equation for the surface obtained by rotating the parabola y = x2 about the y-axis.

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 erig

Selutioa: The serace ef rotatiea is a parakobid with ies major axis along the y-sis ne vertex of the parabekid is al the erig 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

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