MHT CET · Maths · Pair of Lines
The joint equation of two lines through the origin each making an angle of \(30^{\circ}\) with the \(\mathrm{Y}\) - axis is
- A \(x^{2}-3 y^{2}=0\)
- B \(x^{2}+3 y^{2}=0\)
- C \(x^{2}-y^{2}=0\)
- D \(\cdot 2 x^{2}-3 y^{2}=0\)
Answer & Solution
Correct Answer
(C) \(x^{2}-y^{2}=0\)
Step-by-step Solution
Detailed explanation
\(\therefore\) Slope of lines are \(=m_{1}=\tan 60^{\circ}=\sqrt{3}\) and \(\mathrm{m}_{2}=\tan 120^{\circ}=\tan \left(90^{\circ}+30^{\circ}\right)=-\sqrt{3}\)
Their equations are \(y=\sqrt{3} x\) and \(y=-\sqrt{3} x\) i.e. \(\sqrt{3} x-y=0\) and \(\sqrt{3} x+y=0\)
Joint equation is \((\sqrt{3} x-y)(\sqrt{3} x+y)=0 \Rightarrow 3 x^{2}-y^{2}=0\)
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