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AP EAMCET202318 May 2023Morning ShiftMathematicsCircleActual

If x+y-1=0 and 2 x-y+1=0 are conjugate lines with respect to a circle x^2+y^2-4 x+2 f y-1=0 , then f=

Options

  1. A-1 or 3
  2. B1 or 2
  3. C-2 or 0
  4. D-1 or 2

Correct answer

C. -2 or 0

Step-by-step solution

Conjugate lines are : x+y-1=0,2 x-y+1=0 l ₁=1, ~m ₁=1, n ₁=-1, l ₂=2, ~m ₂=-1, n ₂=1 aligned & g=-2, c=-1 & Radius, R= f^2+4+1 = f^2+5 aligned Now, the condition for the conjugate lines : aligned & R ^2 ( l ₁ l ₂+ m ₁ ~m ₂ )= ( l ₁ ~g + m ₁ f - n ₁ ) ( l ₂ ~g + m ₂ f - n ₂ ) & ( f ^2+5 )(1.2+1(-1))=(1(-2)+1 f +1)(2(-2)+(-1) & f -1) & f ^2+5=( f -1)(- f -5) & f ^2+2 f =0 & f =0 or -2 . aligned

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