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Math Help - Show that a certain parametrization is a circle

  1. #1
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    Show that a certain parametrization is a circle

    Hey, a pretty basic one here:

    Show that the curve given by r = a*cos(t)sin(t)i +a*sin^2(t)j + a*cos(t)k (0<t<pi/2)
    lies on a sphere with center at the origin. I have to admit that short of simple plotting I'm rather uncertain at how to tackle this. A hint or two would be great!
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  2. #2
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    Re: Show that a certain parametrization is a circle

    Show that the coordinates (x(t), y(t), z(t)) on the curve satisfy the equation of a sphere.
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  3. #3
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    Re: Show that a certain parametrization is a circle

    to amplify what emakarov said, square each coordinate and add them..what do you get?
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  4. #4
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    Re: Show that a certain parametrization is a circle

    You titled this "show that a certain parameterization is a circle". Of course, there are many "non-circle" curves that lie on a sphere. But once you have identified the center of the sphere, you can use that and two points on the curve to determine a plane and then show that the curve also lies on that plane (satisfies the equation of the plane).
    Last edited by HallsofIvy; December 20th 2011 at 03:34 PM.
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