I need some help on this problem: Prove that the projection into the xy plane of the intersection of the plane z = y and the paraboloid z = x^2 + y^2 is a circle
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Originally Posted by messianic I need some help on this problem: Prove that the projection into the xy plane of the intersection of the plane z = y and the paraboloid z = x^2 + y^2 is a circle Substitute $\displaystyle z=y$ into the $\displaystyle z=x^2+y^2$ to get $\displaystyle y=x^2+y^2\implies x^2+y^2-y=0$. Completing the square gives $\displaystyle x^2+\left(y-\tfrac{1}{2}\right)^2=\tfrac{1}{4}$, which is a circle. Does this make sense?
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