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Question: Answered & Verified by Expert
The separate equations of the lines represented by the equation
$3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$ are
MathematicsPair of LinesMHT CETMHT CET 2020 (15 Oct Shift 1)
Options:
  • A $x-\sqrt{3} y=0$ and $3 x+\sqrt{3} y=0$
  • B $x+\sqrt{3} y=0$ and $3 x+\sqrt{3} y=0$
  • C $x-\sqrt{3} y=0$ and $3 x-\sqrt{3} y=0$
  • D $x+\sqrt{3} y=0$ and $3 x-\sqrt{3} y=0$
Solution:
2404 Upvotes Verified Answer
The correct answer is: $x-\sqrt{3} y=0$ and $3 x+\sqrt{3} y=0$
$3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$
$3 x^{2}-3 \sqrt{3} x y+\sqrt{3} x y-3 y^{2}=0 \Rightarrow 3 x(x-\sqrt{3} y)+\sqrt{3} y(x-\sqrt{3} y)=0$
$(3 x+\sqrt{3} y)(x-\sqrt{3} y)=0 \Rightarrow 3 x+\sqrt{3} y=0, \quad x-\sqrt{3} y=0$

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