Find an Equation for the Surface Obtained by Rotating the Parabola y = x2 About the y-axis

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

Answer: y = x^2 + z^2


Rotate y = x^2 around the y-axis

When rotated the traces parallel to the xz-plane are circles. So the equation should be that of a circle when y = k.

k = x^2

we just have to add a + z^2

y = x^2 + z^2

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

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