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AP EAMCET2008MathematicsParabola

If 2 x+3 y+12=0 and x-y+4 =0 are conjugate with respect to the parabola y^2=8 x , then is equal to

Options

  1. A2
  2. B-2
  3. C3
  4. D-3

Correct answer

D. -3

Step-by-step solution

Using the condition that if two lines l₁ x+m₁ y+n₁=0 and l₂ x+m₂ y+n₂=0 are conjugate w.r.t. parabola y^2=4 a x , then l₁ n₂+l₂ n₁=2 a m₁ m₂ Given conjugate lines are 2 x+3 y+12=0 and x-y+4 =0 and equation of parabola is y^2=8 x . Here, l₁=2, m₁=3, n₁=12 ; l₂=1, m₂=-1 , n₂=4 and a=2 From Eq. (i), gathered 2 4 +1 12=2 2 3 (-1) 8 =-12-12 =-3 gathered

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