The equation of the chord of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ which bisects at the point $(5, - 3)$ is-

2 x - y + 7 = 0

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2 x + 4 y - 7 = 0

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2 x + y - 7 = 0

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2 x - y - 7 = 0

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Solution

The correct option is C $2 x + y - 7 = 0$
$x^{2} + y^{2} - 6 x + 3 y = 0$ $(5, - 3)$
$(3, - 4)$ Slope $= \frac{- 3 + 4}{5 - 3} = \frac{1}{2}$
slope of chord $= - 2$
$- 2 (x - 5) = (y + 3)$
$- 2 x + 10 = y + 3$
$2 x + y = 7$

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Similar questions

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

x^{2} + y^{2} + 2 x - 4 y - 11 = 0

2 x - y + 3 = 0

x^{2} + y^{2} + 2 x - 4 y - 11 = 0

2 x - y + 3 = 0

x^{2} + y^{2} - 8 x - 2 y + 12 = 0

- 1

x^{2} + y^{2} = r^{2}

(2, 3)

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