Find the equation of chord of $x^{2} - y^{2} = 9$ which is bisected at (5, -3).

5x + 3y + 16 = 0

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5x + 3y - 16 = 0

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3x + 5y + 16 = 0

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3x + 5y - 16 = 0

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Solution

The correct option is C 5x + 3y - 16 = 0
Equation of chord bisected at a given point is $T = S^{'}$
So the equation of chord of given hyperbola bisected at $(5, - 3)$ is
$x (5) - y (- 3) - 9 = {(5)}^{2} - {(- 3)}^{2} - 9 5 x + 3 y = 25 - 9 5 x + 3 y = 16 5 x + 3 y - 16 = 0$
So option $C$ is correct

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