"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 4r2 is equal to ________"

Question

Accepted Answer

"Let P(h, k)

Given

PA = 3PB

PA² = 9PB²

$\Rightarrow$ (h $-$ 5)² + k² = 9[(h + 5)² + k²]

$\Rightarrow$ 8h² + 8k² + 100h + 200 = 0

$\therefore$ Locus

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

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

$\therefore$ ${r^2} = {\left( {{{ - 25} \over 4}} \right)^2} - 25$

$= {{625} \over {16}} - 25$

$= {{225} \over {16}}$

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

After Round of 4r² = 56"

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 4r² is equal to ________

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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 4r2 is equal to ________

Solution

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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 4r² is equal to ________