Question: Consider the intersection of the paraboloid [tex]z = x^2 + y^2[/tex] with the plane [tex]x - 2y = 0[/tex]. Find a parametrization of the curve of intersection and verify that it lies in each surface.(adsbygoogle = window.adsbygoogle || []).push({});

How I went about it:

[tex]x = 2y[/tex]

[tex]z = (2y)^2 + y^2 = 5y^2[/tex]

Set [tex]y = t[/tex], then

[tex]x = 2t[/tex]

[tex]y = t[/tex]

[tex]z = 5t^2[/tex]

I don't know that my answer is wrong, I'm just not certain if I am going about it the correct way. If someone could let me know I would appreciate it. Thanks.

Steve

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# Intersection of a paraboloid and a plane

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