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Math Help - Parametric Representation of a curve

  1. #1
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    Parametric Representation of a curve

    Obtain cartesian equation of the curve

    x= 2cos^(2)r
    y= 3sin^(2)r

    0 less than/equal R less than/equal to 2 pi

    I dont know what to do....! Help me please!
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  2. #2
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    x = 2\cos^{2} r \quad \Rightarrow \quad \frac{x}{2} = \cos^{2} r

    y = 3\sin^{2} r \quad \Rightarrow \quad \frac{y}{3} = \sin^{2} r

    Add the equations:
    \frac{x}{2} + \frac{y}{3} = \underbrace{\cos^{2} r + \sin^{2} r}_{1}

    etc.

    Make sure you pay attention to the restriction of r and how it affects the domain and range of the cartesian curve.
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