The locus of centres of the circles which cut the circles $x^{2} + y^{2} + 4 x - 6 y + 9 = 0$ and $x^{2} + y^{2} - 5 x + 4 y + 2 = 0$ orthogonally is

3 x + 4 y - 5 = 0

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9 x - 10 y + 7 = 0

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9 x + 10 y - 7 = 0

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9 x - 10 y + 11 = 0

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Solution

The correct option is B $9 x - 10 y + 7 = 0$
The required locus will be the radical axis
$S_{1} - S_{2} = 0$
$(x^{2} + y^{2} + 4 x - 6 y + 9) - (x^{2} + y^{2} - 5 x + 4 y + 2) = 0$
$9 x - 10 y + 7 = 0$

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The locus of the centres of the circles which cut the circles $x^{2} + y^{2} + 4 x - 6 y + 9 = 0 a n d x^{2} + y^{2} - 5 x + 4 y - 2 = 0$ orthogonally is

Q. The locus of the centres of the circles which cut the circles

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and

x^{2} + y^{2} - 5 x + 4 y - 2 = 0

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The locus of centres of the circles which cut the circles x2+y2+4x−6y+9=0 and x2+y2−5x+4y+2=0 orthogonally is

The correct option is B 9x−10y+7=0The required locus will be the radical axisS1−S2=0(x2+y2+4x−6y+9)−(x2+y2−5x+4y+2)=09x−10y+7=0

The locus of centres of the circles which cut the circles $x^{2} + y^{2} + 4 x - 6 y + 9 = 0$ and $x^{2} + y^{2} - 5 x + 4 y + 2 = 0$ orthogonally is

The correct option is B $9 x - 10 y + 7 = 0$
The required locus will be the radical axis
$S_{1} - S_{2} = 0$
$(x^{2} + y^{2} + 4 x - 6 y + 9) - (x^{2} + y^{2} - 5 x + 4 y + 2) = 0$
$9 x - 10 y + 7 = 0$