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Math Help - Ellipse question

  1. #1
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    Ellipse question

    I'm stuck on the following question:

    The point P(7cost, 5sint) is on the ellipse with equation [(x^2)/49]+[(y^2)/25]=1. The line through P parallel to the y-axis meets the x-axis at X. The point Q is on the line XP produced so that XQ=2XP. Find, in cartesian form, an equation of the locus of Q, as t varies.

    Could someone help please?
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  2. #2
    Senior Member JaneBennet's Avatar
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    Isnít Q just (7\cos{t},10\sin{t})?

    The locus would be the ellipse \frac{x^2}{49}+\frac{y^2}{100}=1.
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  3. #3
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    I have drawn the graphs for you.
    Now you finish it off.
    Attached Thumbnails Attached Thumbnails Ellipse question-ellpi.gif  
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  4. #4
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    Hello, free_to_fly!

    Did you make a sketch?


    The point P(7\cos t,\,5\sin t) is on the ellipse: . \frac{x^2}{49} + \frac{y^2}{25}\:=\:1

    The line through P parallel to the y-axis meets the x-axis at X.

    The point Q is on the line XP produced so that: \overline{XQ}\:=\:2\!\cdot\!\overline{XP}

    Find, in cartesian form, an equation of the locus of Q as t varies.
    Code:
                        |           * Q
                        |           :
                        |           :
                      * * *         :
                 *      |      *    :
            *           |           * P
           *            |        *  :*
                        |     *     :
          *             |  * t      : *
        - * - - - - - - + - - - - - + * -
          *             |           X *
                        |
           *            |            *
            *           |           *
                 *      |      *
                      * * *
                        |

    I totally agree with Jane . . .

    Q has the same x-coordinate as P
    . . and has twice the y-coordinate.

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  5. #5
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    Quote Originally Posted by Soroban View Post
    I totally agree with Jane . . .[/size]
    Once again I must question what teaching is going on here?
    Why not let the student find this out?
    Is that not what teaching all about?
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