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 )

$x^{2} + y^{2} + 4 x + 3$ = 0 $p (x_{1} y_{1})$ 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 $\to 3 x^{2} + 3 y^{2} + 22 x_{1} + 7$ = 0

$x^{2} + y^{2} + \frac{22}{3} x_{1} + \frac{7}{3}$ = 0

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Similar questions

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

Q. The locus of points from which the lengths of the tangents to the two circles

x^{2} + y^{2} + 4 x + 3 = 0

and

x^{2} + y^{2} - 6 x + 5 = 0

are in the ratio

2 : 3

is a circle with centre

Q. The locus of a point which moves so that the ratio of the length of the tangents to the circles

x^{2} + y^{2} + 4 x + 3 = 0

and

x^{2} + y^{2} - 6 x + 5 = 0

2 : 3

, is

Q. If

P (x_{1}, y_{1})

is a point such that the lengths of the tangents from it to the circles

x^{2} + y^{2} - 4 x - 6 y - 12 = 0

and

x^{2} + y^{2} + 6 x + 18 y + 26 = 0

are in the ratio

2 : 3

then the locus of

P

Q. If a point P is moving such that the lengths of tangents drawn from P to the circles

x^{2} + y^{2} - 4 x - 6 y - 12 = 0

and

x^{2} + y^{2} + 6 x + 18 y + 26 = 0

are in the ratio

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then find the equation of the locus of P.

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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 ) x2+y2+4x+3 = 0 p(x1y1) 1:2 x21+y21+4x1+3x21+y21−6x1+5 = 14 x2+y2−6x+5 = 0 →3x2+3y2+22x1+7 = 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