Q67 / 150 · MHT CET 2022 (07 Aug Shift 1) · Mathematics

The joint equation of two lines passing through the origin and perpendicular to the lines given by $2 x^2+5 x y+3 y^2=0$ is

  • A
    $3 x^2+5 x y+2 y^2=0$
  • Correct answer
    B
    $3 x^2-5 x y+2 y^2=0$
  • C
    $3 x^2-5 x y-2 y^2=0$
  • D
    $2 x^2-5 x y+3 y^2=0$

Solution

$2 x^2+5 x y+3 y^2=0 \Rightarrow(x+y)(2 x+3 y)=0$ lines are $x+y=0$ and $2 x+3 y=0$ so, perpendicular lines are $x-y=0$ and $3 x-2 y=0$ joint equation $(x-y)(3 x-2 y)=0$ $\Rightarrow 3 x^2-5 x y+2 y^2=0$

Hence, the correct answer is option: 'B'.

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