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Math Help - Writing an Equation in Cartesian Coordinates?

  1. #1
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    Writing an Equation in Cartesian Coordinates?

    How do I write an equation in Cartesian coordinates for the points in the plane that satisfy...
    p^2 + psinų = 2cosų
    My guess is...
    p^2 + py = 2x^2
    Am I on the right track?
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  2. #2
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    Quote Originally Posted by kellylanemccann View Post
    How do I write an equation in Cartesian coordinates for the points in the plane that satisfy...
    p^2 + psinų = 2cosų
    My guess is...
    p^2 + py = 2x^2
    Am I on the right track?
    Since x = r\cos{\theta} and y = r\sin{\theta}

    \cos{\theta} = \frac{x}{r} and \sin{\theta} = \frac{y}{r}.


    So p^2 + p\sin{\theta} = 2\cos{\theta}

    p^2 + p\left(\frac{y}{r}\right) = 2\left(\frac{x}{r}\right)

    p^2 + \frac{py}{r} = \frac{2x}{r}

    \frac{py}{r} = \frac{2x}{r} - p^2

    py = 2x - p^2r

    y = \frac{2x}{p} - pr.
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