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If the lines 2 x-y+3=0 and 4 x+k y+3=0 are conjugate with respect to the ellipse 5 x^2+6 y^2-15=0 , then k equals

Options

  1. A1
  2. B2
  3. C3
  4. D6

Correct answer

D. 6

Step-by-step solution

2 x-y+3=0 and 4 x+k y+3=0 are conjugate with respect to ellipse 5 x^2+6 y^2-15=0 We know that a₁ x+b₁ y+c₁=0 and a₂ x+b₂ y+c₂=0 are conjugate with x^2 a^2 + y^2 b =1 Then, a^2 a₁ a₂+b^2 b₁ b₂=c₁ c₂ Here, a₁=2, b₁=-1, c₁=3 aligned & a₂=4, b₂=k, c₂=3 & a^2= 15 5 , b^2= 15 6 aligned 15 5 (2)(4)- ( 15 6 )(k)=9 k=6

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