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Math Help - need help with polar equations.

  1. #1
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    need help with polar equations.

    How do i create an equation for a parabola in a polar plane with one focus at (0, 0) and a vertex at (-3, -Pi /2)?
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  2. #2
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    Hello, kaleigh.thomas!

    How do i create an equation for a parabola in a polar plane
    with its focus at (0, 0) and its vertex at \left(\text{-}3,\:\text{-}\frac{\pi}{2}\right) ?
    You are expected to be familiar with polar equations of conics.


    A conic with its focus at (0,0) has the form:

    . . r \;=\;\frac{ke}{1 +e\sin\theta}\:\text{ or }\:\frac{ke}{1 + e\cos\theta}\quad\text{ where: }\;\begin{Bmatrix}e < 1 & \text{ellipse} \\ e = 1 & \text{parabola} \\ e > 1 & \text{hyperbola} \end{Bmatrix}


    From the given information, we know the orientation of the parabola.
    Code:
                    |
                    *
               *    |    *
            *       |       *
      - - * - - - - + - - - - * - -
         *          |          *
                    |
        *           |           *
                    |

    We know that e = 1, and the parabola is "vertical".
    Its equaton contains \sin\theta.

    For the vertex to be at \left(3,\,\tfrac{\pi}{2}\right), we have k = 6.

    . . Therefore: . r \;=\;\frac{6}{1+\sin\theta}

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