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Math Help - Parametric equation for a curve

  1. #1
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    Parametric equation for a curve

    If a = 6 and b = 5, find parametric equations for the curve that consists of all possible positions of the point P in the figure, using the angle θ as the parameter. The line segment AB is tangent to the larger circle.
    x(θ) = ?
    y(θ) = ?
    and θ is in between 0 and 2pi

    i found the picture on the internet, this isn't my assignment but the curve on my assignment is the exact same as #4 from here:
    http://www.iit.edu/~maslanka/Rec3F08.pdf

    i tried doing this:
    x = a + b
    y = asin(θ)

    but i didn't knwo what to do from there. add them maybe? but how would you get rid of sin(θ)? i'm confused lol. please help someone.
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  2. #2
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    Hello, CenturionMonkey!

    If a = 6 and b = 5, find parametric equations for the curve that consists
    of all possible positions of the point P in the figure, using \theta
    as the parameter. .The line segment AB is tangent to the larger circle.

    . . \begin{array}{ccc}x&=& f(\theta) \\ y &=& g(\theta) \end{array}\quad \text{for }0 \leq\theta \leq 2\pi


    I won't try to copy the diagram this time.

    In right triangle OAB\!:\;\;\sec\theta \:=\:\frac{OB}{OA} \:=\:\frac{x}{6} \quad\Rightarrow\quad x \:=\:6\sec\theta

    In the smallest right triangle: . \sin\theta \:=\:\frac{y}{5} \quad\Rightarrow\quad y \:=\:5\sin\theta


    Therefore: . \begin{Bmatrix}x &=& 6\sec\theta \\ y &=& 5\sin\theta \end{Bmatrix}

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  3. #3
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    oh yeah that makes perfect sense. I didn't realize that was a right triangle. lol silly me. thanks
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