Let a point P be such


Let a point $\mathrm{P}$ be such that its distance from the point $(5,0)$ is thrice the distance of $\mathrm{P}$ 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 (Round off to the nearest integer)


Let $P(h, k)$


$P A=3 P B$

$P A^{2}=9 P B^{2}$


$\Rightarrow 8 h^{2}+8 k^{2}+100 h+200=0$

$\therefore$ Locus

$x^{2}+y^{2}+\left(\frac{25}{2}\right) x+25=0$

$\therefore c \equiv\left(\frac{-25}{4}, 0\right)$




$\therefore 4 r^{2}=4 \times \frac{225}{16}=\frac{225}{4}=56.25$

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