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Thread: 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

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


    Also find a parametrization of the form $\displaystyle x=x(t), y=y(t)$ for $\displaystyle r=1-cos\theta, 0\leq \theta \leq 2\pi$
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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

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


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

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

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