Hello, free_to_fly!
Did you make a sketch?
The point $\displaystyle P(7\cos t,\,5\sin t)$ is on the ellipse: .$\displaystyle \frac{x^2}{49} + \frac{y^2}{25}\:=\:1$
The line through $\displaystyle P$ parallel to the yaxis meets the xaxis at $\displaystyle X.$
The point $\displaystyle Q$ is on the line $\displaystyle XP$ produced so that: $\displaystyle \overline{XQ}\:=\:2\!\cdot\!\overline{XP}$
Find, in cartesian form, an equation of the locus of $\displaystyle Q$ as $\displaystyle t$ varies. Code:
 * Q
 :
 :
* * * :
*  * :
*  * P
*  * :*
 * :
*  * t : *
 *       +      + * 
*  X *

*  *
*  *
*  *
* * *

I totally agree with Jane . . .
$\displaystyle Q$ has the same xcoordinate as $\displaystyle P$
. . and has twice the ycoordinate.