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Math Help - Parametrize the curve of intersection

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    Parametrize the curve of intersection

    Parametrize the curve of intersection of the sphere x^2+y^2+z^2=1 and the elliptic cylinder x^2+2z^2=1. Find the total length of this intersection curve.
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    Quote Originally Posted by jonnyp2009 View Post
    Parametrize the curve of intersection of the sphere x^2+y^2+z^2=1 and the elliptic cylinder x^2+2z^2=1. Find the total length of this intersection curve.

    Note you can solve the 2nd equation for z^2 to get

    z^2=\frac{1-x^2}{2}

    sub this into the first equation to get

    x^2+y^2+\frac{1}{2}-\frac{x^2}{2}=1

    \frac{x^2}{2}+y^2=\frac{1}{2} \iff x^2+\frac{y^2}{(\frac{1}{\sqrt{2}})^2}=1

    This is an equation of an ellipse...

    This should get you started
    Last edited by TheEmptySet; December 8th 2009 at 07:34 AM. Reason: Missing radical
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    ok thanks i got it now, i then get x=cost and solve for y then plug them both into sphere equation for z

    so y=1/sqrt(2)sint
    and z=1/sqrt(2)sint
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