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Three Dimensional Geometry

Question
CBSEENMA12036138

The lines p(p2+ 1) x – y + q = 0 and (p2+ 1)2x + (p2+ 1) y + 2q = 0 are
perpendicular to a common line for

  • no value of p

  • exactly one value of p

  • exactly two values of p

  • more than two values of p 

Solution

B.

exactly one value of p

straight p left parenthesis straight p squared space plus 1 right parenthesis space equals space fraction numerator negative left parenthesis straight p squared space plus 1 right parenthesis squared over denominator straight p squared plus 1 end fraction
y = q
x + y + 2q = 0
⇒ p = –1