Thread: 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?

Isn’t Q just ?

The locus would be the ellipse .

I have drawn the graphs for you.
Now you finish it off.

Hello, free_to_fly!

Did you make a sketch?

The point is on the ellipse: .

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

The point is on the line produced so that:

Find, in cartesian form, an equation of the locus of as varies.

Code:

                    |           * Q
                    |           :
                    |           :
                  * * *         :
             *      |      *    :
        *           |           * P
       *            |        *  :*
                    |     *     :
      *             |  * t      : *
    - * - - - - - - + - - - - - + * -
      *             |           X *
                    |
       *            |            *
        *           |           *
             *      |      *
                  * * *
                    |

I totally agree with Jane . . .

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

Originally Posted by Soroban

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?