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Math Help - Coordinates

  1. #1
    Len
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    Coordinates

    Would anyone mind telling me how I convert coordinates to xy. The case I'm on is

    r=\frac{1}{1+cos\theta}


    Also find a parametrization of the form x=x(t), y=y(t) for r=1-cos\theta,   0\leq \theta \leq 2\pi
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  2. #2
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    Quote Originally Posted by Len View Post
    Would anyone mind telling me how I convert coordinates to xy. The case I'm on is

    r=\frac{1}{1+cos\theta}


    Also find a parametrization of the form x=x(t), y=y(t) for r=1-cos\theta,   0\leq \theta \leq 2\pi
    r\cos \theta = x.
    Thus, r = \frac{1}{1+\frac{x}{r}} \implies r = \frac{r}{r+x} \implies 1 = \frac1{r+x}

    Therefore, r+x = 1 \implies \sqrt{x^2+y^2} = 1-x

    Square, x^2+y^2 = (1-x)^2 \implies x^2+y^2 = 1 - 2x + x^2 \implies y^2 = 1-2x
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