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  • Let a point P be such that its distance from the point is thrice the distance of P from the point

Let a point P be such that its distance from the point \left ( 5,0 \right ) is thrice the distance of P from the point \left ( -5,0 \right ). If the locus of the point P is a circle of radius r, then 4r^{2} is equal to ________.
Option: 1 56.25
Option: 2 15.25
Option: 3 15
Option: 4 25.25

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\begin{aligned} &\text { Let point is }(\mathrm{h}, \mathrm{k})\\ &\text { So, } \sqrt{(\mathrm{h}-5)^{2}+\mathrm{k}^{2}}=3 \sqrt{(\mathrm{h}+5)^{2}+\mathrm{k}^{2}}\\ &8 x^{2}+8 y^{2}+100 x+200=0\\ &x^{2}+y^{2}+\frac{25}{2} x+25=0 \end{aligned}

\begin{aligned} &r^{2}=\frac{(25)^{2}}{4^{2}}-25\\ &4 r^{2}=\frac{25^{2}}{4}-100\\ &\begin{array}{l} 4 \mathrm{r}^{2}=156.25-100 \\ 4 \mathrm{r}^{2}=56.25 \end{array}\\ &\text {After round of } 4 r^{2}=56 \end{aligned}

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Suraj Bhandari

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