MHT CET · Maths · Pair of Lines
The combined equation of a pair of lines passing through the origin and inclined at \(60^{\circ}\) and \(30^{\circ}\) respectively with \(\mathrm{x}\)-axis is
- A \(\sqrt{3}\left(x^2+y^2\right)=2 x y\)
- B \(\sqrt{3}\left(x^2+y^2\right)=4 x y\)
- C \(4\left(x^2+y^2\right)=\sqrt{3} x y\)
- D \(2\left(x^2+y^2\right)=\sqrt{3} x y\)
Answer & Solution
Correct Answer
(B) \(\sqrt{3}\left(x^2+y^2\right)=4 x y\)
Step-by-step Solution
Detailed explanation
The equation of two required lines are \(y=\sqrt{3} x\) and \(y=\frac{1}{\sqrt{3}} x\) Their combined equation is
\(
(\sqrt{3} x-y)(x-\sqrt{3} y)=0 \text { i.e. } \sqrt{3} x^2-4 x y+\sqrt{3} y^2=0
\)
\(
(\sqrt{3} x-y)(x-\sqrt{3} y)=0 \text { i.e. } \sqrt{3} x^2-4 x y+\sqrt{3} y^2=0
\)
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