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AP EAMCET202125 Aug 2021Morning ShiftMathematicsCircleActual

If (6,-k) and (-3,2) are conjugate points with respect to circle x^2+y^2+6 x+4 y+12=0 , then k equals

Options

  1. A-7 4
  2. B7 4
  3. C4 7
  4. D-4 7

Correct answer

B. 7 4

Step-by-step solution

Points (6,-k) and (-3,2) are conjugate points to the circle x^2+y^2+6 x+4 y+12=0 We know that if (x₁, y₁ ) and (x₂, y₂ ) are conjugate points of circle x^2+y^2+2 g x+2 f y+c=0 Then, x₁ x₂+y₁ y₂+g (x₁+x₂ )+f (y₁+y₂ )+c=0 (6)(-3)+(-k)(2)+3(6-3)+2(-k+2)+12=0 -18-2 k+9-2 k+4+12=0 4 k=7 k=7 / 4

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