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AP EAMCET202421 May 2024Evening ShiftMathematicsPair of LinesActual

If the pair of lines represented by 3 x^2-5 x y+P y^2=0 and 6 x^2-x y-5 y^2=0 have one line in common, then the sum of all possible values of P is

Options

  1. A33 4
  2. B17 4
  3. C- 33 4
  4. D- 17 4

Correct answer

D. - 17 4

Step-by-step solution

6 x^2-x y-5 y^2=0 (6 x+5 y)(x-y)=0 y=x or y= -6 x 5 When y=x, 3 x^2-5 x^2+P x^2=0 P=2 When y=- 6 x 5 ; 3 x^2-5 x ( -6 x 5 )+ 36 x^2 25 P=0 9+ 36 P 25 =0 P= -25 4 ; Sum of values of P=2- 25 4 = -17 4 .

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