The equation of the diameter of the circle $x^{2} + y^{2} + 2 x - 4 y - 11 = 0$ which bisects the chords intercepted on the line $2 x - y + 3 = 0$ is

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x+2y+3=0

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Solution

The correct option is C

We know that the diameter will be perpendicular to the chord because it bisects the chord. Hence the equation of diameter $x + 2 y + k = 0$ .............(i)

But (i) also passes through the centre of circle (-1,2). Therefore, $- 1 + 4 + k = 0 \Rightarrow k + - 3$ .

Hence the required equation is $x + 2 y - 3 = 0$

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Equation of the diameter of the circle $x^{2} + y^{2} - 2 x + 4 y = 0$ which passes through the origin is

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