For a circle $x^{2} + y^{2} = 81$ , what is the equation of chord whose mid-point is $(- 2, 3)$ ?

2 x - 3 y + 13 = 0

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3 x - 2 y + 13 = 0

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2 x - 3 y - 13 = 0

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2 x + 3 y + 13 = 0

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Solution

The correct option is A $2 x - 3 y + 13 = 0$
$∵$ Equation of the required chord is $T = S^{^{'}}$
$∴ - 2 x + 3 y - 9 = 4 + 9 - 9$
$\Rightarrow - 2 x + 3 y = 4 + 9$
$\Rightarrow 2 x - 3 y + 13 = 0$ .

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