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Math Help - Help with Planes and Paraboloids

  1. #1
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    Help with Planes and Paraboloids

    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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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by messianic View Post
    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 z=y into the z=x^2+y^2 to get y=x^2+y^2\implies x^2+y^2-y=0.

    Completing the square gives x^2+\left(y-\tfrac{1}{2}\right)^2=\tfrac{1}{4}, which is a circle.

    Does this make sense?
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