Which of the following is a point on the common chord of the circle $x^{2} + y^{2} + 2 x - 3 y + 6 = 0$ and $x^{2} + y^{2} + x - 8 y - 13 = 0$

(1, 4)

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(1, - 2)

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(1, - 4)

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(1, 2)

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Solution

The correct option is C $(1, - 4)$
The equation of the common chord of the given circles is given by $(x^{2} + y^{2} + 2 x - 3 y + 6) - (x^{2} + y^{2} + x - 8 y - 13) = 0$
i.e. $x + 5 y + 19 = 0$
Out of the four options, the point satisfying the above equation is $(1, - 4)$

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