The separate equations of the lines represented by the equation $3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$ are

The separate equations of the lines represented by the equation $3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$ are
  1. $x-\sqrt{3} y=0$ and $x+\sqrt{3} y=0$
  2. $x+\sqrt{3} y=0$ and $x+\sqrt{3} y=0$
  3. $x-\sqrt{3} y=0$ and $x-\sqrt{3} y=0$
  4. $x+\sqrt{3} y=0$ and $x-\sqrt{3} y=0$

Solution

$3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0$ $3 x^{2}-3 \sqrt{3} x y+\sqrt{3} x y-3 y^{2}=0 \Rightarrow 3 x(x-\sqrt{3} y)+\sqrt{3} y(x-\sqrt{3} y)=0$ $(3 x+\sqrt{3} y)(x-\sqrt{3} y)=0 \Rightarrow 3 x+\sqrt{3} y=0, \quad x-\sqrt{3} y=0$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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