Multiple choice

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

  1. $2 x + y - 7 = 0$
  2. $x + 2 y + 1 = 0$
  3. $2 x - y - 13 = 0$
  4. $x - 2 y - 11 = 0$
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A Correct answer
Explanation

The equation of a chord bisected at (x1, y1) is T = S1. T = x*x1 + y*y1 - 3(x+x1) + 4(y+y1). S1 = x1^2 + y1^2 - 6*x1 + 8*y1. Substituting (5, -3) gives 5x - 3y - 3(x+5) + 4(y-3) = 25 + 9 - 30 - 24. 2x + y - 27 = -20. 2x + y - 7 = 0.

AI explanation

The equation of a chord bisected at a given point is T = S1. For the circle x^2 + y^2 - 6x + 8y = 0 and the point (5, -3), the equation is 5x - 3y - 3(x + 5) + 4(y - 3) = 25 + 9 - 30 - 24. Simplifying this gives 2x + y - 7 = 0.

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