The value of ' p ' for which the equation x 2 + p x y + y 2 - 5 x - 7 y + 6 = 0 represents a pair of…

The value of 'p' for which the equation x2+pxy+y2-5x-7y+6=0 represents a pair of straight lines, is
  1. 52
  2. 5
  3. 2
  4. 25

Solution

Given equation

x2+pxy+y2-5x-7y+6=0

Will represent a pair of straight lines, if ∆=0

⇒1⋅1⋅6+2-72-52p2-1-722-1-522-6p22=0

⇒ 6+35p4-494-254-6p24=0

⇒ 35p-50-6p2=0

⇒ 2p-53p-10=0

⇒ p=52,103

Asked in: AP EAMCET 2021 (20 Aug Shift 2)

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