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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