If the ratio of the lengths of tangents from a point to the circles $x^{2} + y^{2} + 4 x + 3$ = 0, $x^{2} + y^{2} - 6 x + 5$ = 0 is 1:2 then the locus of P is a circle whose centre is

(-11/3 , 0 )

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(-22/3 , 0 )

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(-11 , 6 )

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(-11/5 , 0 )

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Solution

The correct option is A
(-11/3 , 0 )

$p (x_{1} y_{1})$
$x^{2} + y^{2} + 4 x + 3$ = 0
$\to 3 x^{2} + 3 y^{2} + 22 x_{1} + 7$ = 0
Length of the tangents are in the ratio 1:2
$\frac{x_{1}^{2} + y_{1}^{2} + 4 x_{1} + 3}{x_{1}^{2} + y_{1}^{2} - 6 x_{1} + 5}$ = $\frac{1}{4}$
$x^{2} + y^{2} - 6 x + 5$ = 0
$x^{2} + y^{2} + \frac{22}{3} x_{1} + \frac{7}{3}$ = 0

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If the ratio of the lengths of tangents from a point to the circles $x^{2} + y^{2} + 4 x + 3$ = 0, $x^{2} + y^{2} - 6 x + 5$ = 0 Is 1:2 then the locus of P is a circle whose centre is

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If the ratio of the lengths of tangents from a point to the circles x2+y2+4x+3 = 0,x2+y2−6x+5 = 0 is 1:2 then the locus of P is a circle whose centre is

The correct option is A (-11/3 , 0 ) p(x1y1) x2+y2+4x+3 = 0 →3x2+3y2+22x1+7 = 0 Length of the tangents are in the ratio 1:2 x21+y21+4x1+3x21+y21−6x1+5 = 14 x2+y2−6x+5 = 0 x2+y2+223x1+73 = 0

If the ratio of the lengths of tangents from a point to the circles $x^{2} + y^{2} + 4 x + 3$ = 0, $x^{2} + y^{2} - 6 x + 5$ = 0 is 1:2 then the locus of P is a circle whose centre is