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COMEDK2013MathematicsCircle

The value of k so that x²+y²+k x+4 y+2=0 and 2 (x²+y² )-4 x-3 y+k=0 cut orthogonally is

Options

  1. A10 3
  2. B- 8 3
  3. C- 10 3
  4. D8 3

Correct answer

C. - 10 3

Step-by-step solution

Given, circles can be written as x²+y²+k x+4 y+2=0 and x²+y²-2 x- 3 2 y+ k 2 =0 Since, both circles are orthogonal, then 2 g₁ g₂+2 f₁ f₂=c₁+c₂ -k-3=2+ k 2 3 k 2 =-5 k=- 10 3

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