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Math Help - Calc Cartesian Equation

  1. #1
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    Calc Cartesian Equation

    A curve is parametrized by x=t, y=the square root of (t+2), t is greater than or equal to -2.
    Write a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?
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  2. #2
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    Hello, SoYah!

    A curve is parametrized by: . \begin{array}{cccc}x\:=\:t & {\color{blue}[1]}\\ y\:=\: \sqrt{t+2} & {\color{blue}[2]}\end{array}\;\:\text{ for }x \geq -2

    (a) Write a Cartesian equation for a curve that contains the parametrized curve.

    Substitute [1] into [2]: . y \:=\:\sqrt{x+2} \quad\Rightarrow\quad x \:=\:y^2-2

    This is a parabola that opens to the right, vertex at (-2,0).




    (b) What portion of the graph of the Cartesian equation is traced by the parametrized curve?

    The parametric equations determine the upper half of the parabola.

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