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 $\mathrm{r}$, then $4 \mathrm{r}^{2}$ is equal to
Solution:
Jet noint is (h. k)
So, $\sqrt{(h-5)^{2}+k^{2}}=3 \sqrt{(h+5)^{2}+k^{2}}$
$8 x^{2}+8 y^{2}+100 x+200=0$
$x^{2}+y^{2}+\frac{25}{2} x+25=0$
$r^{2}=\frac{(25)^{2}}{4^{2}}-25$
$4 \mathrm{r}^{2}=\frac{25^{2}}{4}-100$
$4 r^{2}=156.25-100$
$4 r^{2}=56.25$
After round of $4 \mathrm{r}^{2}=56$