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Math Help - Converting polar equation to rectangular

  1. #1
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    Converting polar equation to rectangular

    I know that I usually use r^2=x^2+y^2, x = r cos(t) and y = r sin(t) to convert polar equations to rectangular, but I seem to come to the correct solution.

    r(\theta) = \frac{e \cdot p}{1+e \cdot  cos(\theta)}

    e and p are constants

    The polar equation is supposed to be an ellipse, but the solution I came up with doesn't seem correct.

    x = r \cdot cos(t)

    r = \frac{e \cdot p}{1 + e \frac{x}{r}}

    r(1+e \frac{x}{r}) = e \cdot p

    r + e \cdot x = ep

    r = e \cdot x - e \cdot p

    r = e ( x - p)

    r^{2} = ( e ( x-p))^{2}

    x^{2}+y^{2} = ( e ( x-p))^{2}

    Any ideas?
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  2. #2
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    You have a small error in the fifth line. It should be r=ep-ex. Other than that it looks correct. Your final answer is an ellipse - it's just not in standard form. You can put it in standard form by multiplying everything out, bringing everything over to the left and completing the square.
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