If $y + 3 x = 0$ is the equation of a chord of the circle, $x^{2} + y^{2} - 30 x = 0$ , then the equation of the circle with this chord as diameter is

x^{2} + y^{2} - 3 x - 9 y = 0

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x^{2} + y^{2} + 3 x + 9 y = 0

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x^{2} + y^{2} - 3 x + 9 y = 0

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x^{2} + y^{2} + 3 x - 9 y = 0

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Solution

The correct option is C $x^{2} + y^{2} - 3 x + 9 y = 0$
$y + 3 x = 0 x^{2} + y^{2} - 30 x = 0 \Rightarrow x^{2} + (- 3 x)^{2} - 30 x = 0 \Rightarrow 10 x (x - 3) = 0 \Rightarrow x = 0, 3 \Rightarrow x = 0, y = 0 x = 3, y = - 9$
Equation of the circle whose end points of the diameter are $(0, 0)$ and $(3, - 9)$ is
$(x - 3) (x - 0) + (y + 9) (y - 0) = 0 \Rightarrow x^{2} + y^{2} - 3 x + 9 y = 0$

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