The equation of diameter of the circle $(x - 2)^{2} + (y + 1)^{2} = 16$ which bisect the chord cut off by the circle on the line $x - 2 y - 3 = 0$ is

2 x - y + 3 = 0

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2 x + y - 3 = 0

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2 x + y + 3 = 0

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None of these

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Solution

The correct option is B $2 x + y - 3 = 0$
Given, equation of the circle is $(x - 2)^{2} + (y + 1)^{2} = 16$ and equation of chord is $x - 2 y - 3 = 0$
Perpendicular drawn to the chord from the centre bisects it.
Hence, the diameter which bisects the chord is perpendicular to it.
Equation of the line passing through $(2, - 1)$ with slope $m = - 2$ is $2 x + y - 3 = 0$
$∴$ Required equation of diameter is $2 x + y - 3 = 0$
Hence, option B.

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The equation of diameter of the circle (x−2)2+(y+1)2=16 which bisect the chord cut off by the circle on the line x−2y−3=0 is

The equation of diameter of the circle $(x - 2)^{2} + (y + 1)^{2} = 16$ which bisect the chord cut off by the circle on the line $x - 2 y - 3 = 0$ is