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Leval Curves of a Cone and a Paraboloid

Show that the level curves of the cone z = ( x^(2) + y^(2) )^(1/2) and the paraboloid z = x^(2) + y^(2) are circles.

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Proof. A level curve of a function z=f(x,y) is
where c is a constant. Hence,

(1) For the cone z = ( x^(2) + y^(2) ...

Solution Summary

The level curves of a cone and a paraboloid are shown to be circles.