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Math Help - Parametric equations.

  1. #1
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    Question Parametric equations.

    <Any Help would be greatly appreciated>
    This stuff confuses me

    6. Elimante the parameter and write the corresponding rectangular equation adjustin the domain as necessary for the parametric equations x=2cosų and y=3sinų.

    7. Find a set of parametric equations for the rectangular equation x=3y-2 by using:
    A) x=t
    B) 2-x=t
    Last edited by mr fantastic; May 5th 2009 at 06:36 AM. Reason: Moved from original thread.
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  2. #2
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    Hello, jrose011!

    Here's #6 . . .


    6. Eliminate the parameter: . \begin{array}{c}x \:=\:2\cos\theta \\ y \:=\:3\sin\theta \end{array}
    We have the equations: . \begin{array}{c}\dfrac{x}{2} \:=\:\cos\theta \\ \\[-3mm] \dfrac{y}{3} \:=\:\sin\theta \end{array}

    Square the equations: . \begin{array}{cc}\dfrac{x^2}{4} \:=\:\cos^2\!\theta & {\color{blue}[1]} \\ \\[-3mm] \dfrac{y^2}{9} \:=\:\sin^2\!\theta & {\color{blue}[2]} \end{array}

    \text{Add {\color{blue}[1]} and {\color{blue}[2]}: }\;\frac{x^2}{4} + \frac{y^2}{9} \;=\;\underbrace{\cos^2\!\theta + \sin^2\!\theta}_{\text{This is 1}}

    . . Therefore: . \frac{x^2}{4} + \frac{y^2}{9} \;=\;1 \quad\hdots\;\text{ an ellipse}

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  3. #3
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    Thanks alot! Really helped and makes perfect sense.
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