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BITSAT2011MathematicsCircleActual

For what value of (k ) the circles (x^2+y^2+5 x+3 y+7=0 ) and (x^2+y^2-8 x+6 y+k=0 ) cuts orthogonally

Options

  1. A16
  2. B-18
  3. C-13
  4. D-10

Correct answer

B. -18

Step-by-step solution

Let the two circles be (x^2+y^2+2 g₁ x+2 f₁ y ) (+c₁=0 ) and (x^2+y^2+2 g₂ x+2 f₂ y+c₂=0 ) where (g₁=5 / 2, f₁=3 / 2, c₁=7, g₂=4, f₂=3 ) and ( c ₂= k ) If the two circles intersects orthogonally, then ( aligned & 2~ ( g ₁ ~g ₂+ f ₁ f ₂ )= c ₁+ c ₂ 2 (-10+ 9 2 )=7+ k & 11=7+ k k =-18 aligned )

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