Let  $P$ be a point on the ellipse  $\frac{x^2}{25}+\frac{y^2}{9}=1,$ in first quadrant with focal distance 7 units w.r.t focus  $S\text{'}(-4,0).$ Let  $S\text{'}P$ and perpendicular from focus  $S$ on the tangent at $P$  intersect at  $Q.$ Then which of the following is NOT TRUE ?

Clearly  $S\equiv (4,0);$ Let  $P=(\alpha ,\beta )$
 $\Rightarrow a+e\alpha =7\Rightarrow 5+\frac{4}{5}\alpha =7\Rightarrow \alpha =\frac{5}{2}and\beta =\frac{3\sqrt{3}}{2}$
Hence, equation of tangent at  $P$ is  $\alpha =\frac{5}{2}$  and  $\beta =\frac{3\sqrt{3}}{2}$
As tangent is bisector of angle between  $SP$ and  $S\text{'}P$
$\Rightarrow PQ=PS=3.$  As  $PS+PS\text{'}=10=$ Length of major axis  
When   is variable then  $S\text{'}Q=S\text{'}P+PQ=S\text{'}P+PS=10$
$\Rightarrow$   Variable point  $Q$ is at a fixed distance from  $S\text{'}$
 $\Rightarrow$  Locus is a circle with centre  $S\text{'}$ and radius = 10 units