The equation of the chord of the circle $x^{2} + y^{2} = r^{2}$ passing through $(2, 3)$ and farthest from the centre is

x - 3 y + 7 = 0

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2 x + y - 7 = 0

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2 x + 3 y - 13 = 0

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x + y - 5 = 0

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Solution

The correct option is C $2 x + 3 y - 13 = 0$
The chord which is farthest from the centre $(0, 0)$ and passing through $(2, 3)$ is the chord which has midpoint at $(2, 3)$ , so
$T = S_{1} \Rightarrow 2 x + 3 y - r^{2} = 2^{2} + 3^{2} - r^{2} \Rightarrow 2 x + 3 y - 13 = 0$

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