Prove that rule for surface of revolution is of given value


If we take take a curve z = f(y) in the yz-plane and revolve it about the z-axis, we obtain a surface of revolution in space. What do the level curves look like? Prove that the rule for the surface of revolution thus obtained is z= f(√(x2 + y2)). Use this result to deduce that the equation x2+ y2+ 2x + 2y - z2+ 2 = 0 defines a cone in space.

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Mathematics: Prove that rule for surface of revolution is of given value
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