The radical axis of the circles $x^{2} + y^{2} - 6 x - 4 y + 4 = 0$ and $x^{2} + y^{2} - 14 x - 5 y - 24 = 0$ is

8 x + y - 30 = 0

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8 x + y + 20 = 0

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8 x + 3 y - 20 = 0

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8 x + y + 28 = 0

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Solution

The correct option is D $8 x + y + 28 = 0$
The equation of the radical axis is given by
$C_{1} - C_{2} = 0$
Or
$(x^{2} + y^{2} - 6 x - 4 y + 4) - (x^{2} + y^{2} - 14 x - 5 y - 24) = 0$
$x (14 - 6) + y (5 - 4) + 24 + 4 = 0$
$8 x + y + 28 = 0$

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