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Thread: 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 $\displaystyle x = r\cos{\theta}$ and $\displaystyle y = r\sin{\theta}$

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


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

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

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

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

    $\displaystyle py = 2x - p^2r$

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