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Equation of Radical Axis

Equation of r...

Question

Equation of radical axis of the circles $x^{2} + y^{2} - 3 x - 4 y + 5 = 0$ and $2 x^{2} + 2 y^{2} - 10 x - 12 y + 12 = 0$ is

A

2 x + 2 y - 1 = 0

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B

2 x + 2 y + 1 = 0

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C

x + y + 7 = 0

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D

x + y - 7 = 0

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Solution

The correct option is A $2 x + 2 y - 1 = 0$
Let the equation of circles are
$S_{1} \equiv x^{2} + y^{2} - 3 x - 4 y + 5 = 0$
and $S_{2} \equiv {2 x}^{2} + 2 y^{2} - 10 x - 12 y + 12 = 0$
$\Rightarrow S_{2} \equiv x^{2} + y^{2} - 5 x - 6 y + 6 = 0$
$∴$ The radical axis of two circles be
$S_{1} - S_{2} = 0$
$\Rightarrow {- x}^{2} + y^{2} - 3 x - 4 y + 5 {- x}^{2} - y^{2} + 5 x + 6 y - 6 = 0$
$\Rightarrow 2 x + 2 y - 1 = 0$

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