AP EAMCET · Maths · Pair of Lines
If one of the lines given by the pair of lines \(3 x^2-2 y^2+a x y=0\) is making an angle \(60^{\circ}\) with x -axis then \(\mathrm{a}=\)
- A \(\sqrt{3}\)
- B \(\frac{1}{\sqrt{3}}\)
- C \(3\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(m = \tan(60^{\circ}) = \sqrt{3}\) \(2m^2 - am - 3 = 0\) \(2(\sqrt{3})^2 - a(\sqrt{3}) - 3 = 0\) \(6 - a\sqrt{3} - 3 = 0\) \(3 - a\sqrt{3} = 0\) \(a = \frac{3}{\sqrt{3}} = \sqrt{3}\)
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