MHT CET · Maths · Pair of Lines
The separate equations of the lines represented by the equation
\(3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0\) are
- 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 \(3 x-\sqrt{3} y=0\)
Answer & Solution
Correct Answer
(A) \(x-\sqrt{3} y=0\) and \(3 x+\sqrt{3} y=0\)
Step-by-step Solution
Detailed explanation
\(3 x^{2}-2 \sqrt{3} x y-3 y^{2}=0\)
\(3 x^{2}-3 \sqrt{3} x y+\sqrt{3} x y-3 y^{2}=0 \Rightarrow 3 x(x-\sqrt{3} y)\)\(+\sqrt{3} y(x-\sqrt{3} y)=0\)
\((3 x+\sqrt{3} y)(x-\sqrt{3} y)=0 \Rightarrow 3 x+\sqrt{3} y=0, \quad x\)\(-\sqrt{3} y=0\)
\(3 x^{2}-3 \sqrt{3} x y+\sqrt{3} x y-3 y^{2}=0 \Rightarrow 3 x(x-\sqrt{3} y)\)\(+\sqrt{3} y(x-\sqrt{3} y)=0\)
\((3 x+\sqrt{3} y)(x-\sqrt{3} y)=0 \Rightarrow 3 x+\sqrt{3} y=0, \quad x\)\(-\sqrt{3} y=0\)
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