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Math Help - Parametrically Defined Curves

  1. #1
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    Parametrically Defined Curves

    Describe the following curve:
    r(t)=2cost i +3sint j

    The ans is:

    An Ellipse
    since (x^2)/(2^2)+(y^2)/(3^2) = 1


    I cant see where they get this ans from?
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  2. #2
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    \displaystyle x = 2\cos{t} \implies \cos{t} = \frac{x}{2}


    \displaystyle y = 3\sin{t} \implies \sin{t} = \frac{y}{3}.


    \displaystyle \sin^2{t} + \cos^2{t} = 1

    \displaystyle \left(\frac{y}{3}\right)^2 + \left(\frac{x}{2}\right)^2 = 1

    \displaystyle \frac{y^2}{9} + \frac{x^2}{4} = 1.

    It's an ellipse.
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