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AP EAMCET202315 May 2023Evening ShiftMathematicsStraight LinesActual

The lines p (p^2+1 ) x-y+q=0 and (p^2+1 )^2 x+ (p^2+1 )y+2 q=0 are perpendicular to a line L for

Options

  1. Aexactly one value of p
  2. Bexactly two values of p
  3. Cmore than two values of p
  4. Dno value of p

Correct answer

A. exactly one value of p

Step-by-step solution

For 1st line m₁=p (p^2+1 ) for 2 nd line m ₂=- ( p ^2+1 ) Since, if these two line are perpendicular to the line L then aligned & m ₁= m ₂ & p (p^2+1 )=- (p^2+1 ) p=-1 aligned

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