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COMEDK2023MathematicsPair of Lines

Let the equation of pair of lines y=m₁ x and y=m₂ x can be written as (y-m₁ x ) (y-m₂ x )=0 . Then, the equation of the pair of the angle bisector of the line 3 y^2-5 x y-2 x^2=0 is

Options

  1. Ax^2+5 x y-y^2=0
  2. Bx^2-5 x y+y^2=0
  3. Cx^2-x y+y^2=0
  4. Dx^2+x y-y^2=0

Correct answer

D. x^2+x y-y^2=0

Step-by-step solution

Equation of angles of bisector of pair of straight line, a x^2+2 b x y+b y^2 is x^2-y^2 a-b = x y h For, 3 y^2-5 x y-2 x^2=0a=3, b=-2, h=-5 So, equation of angle bisector is aligned & x^2-y^2 3-(-2) = x y -5 x^2-y^2 5 & = x y -5 x^2-y^2+x y=0 aligned

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