Question

Let a point $P$ be such that its distance from the point (5,0) is thrice the distance of $P$ from the point (-5,0) . If the locus of the point $P$ is a circle of radius $r$, then $4 r ^{2}$ is equal to_________.

Answer 1

Let point is $( h , k )$
So,$\sqrt{( h -5)^{2}+ k ^{2}}=3 \sqrt{( h +5)^{2}+ k ^{2}}$
$8 x^{2}+8 y^{2}+100 x+200=0$
$x^{2}+y^{2}+\frac{25}{2} x+25=0$
$r^{2}=\frac{(25)^{2}}{4^{2}}-25$
$4 r ^{2}=\frac{25^{2}}{4}-100$
$4 r^{2}=156.25-100$
$4 r ^{2}=56.25$
After round of $4 r^{2}=56$