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Pair of Straight Lines — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
Acute angle between the lines represented by $\left(x^2+y^2\right) \sqrt{3}=4 x y$ is
  • ✓
    $\frac{\pi}{6}$
  • B
    $\frac{\pi}{4}$
  • C
    $\frac{\pi}{3}$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{\pi}{6}$
(A) Given equation of pair of lines is $\left(x^2+y^2\right) \sqrt{3}=4 x y$
$\therefore \quad a=\sqrt{3}, h=-2, b=\sqrt{3}$
$\therefore \quad \tan \theta=\left|\frac{2 \sqrt{4-3}}{2 \sqrt{3}}\right|=\frac{1}{\sqrt{3}}$
$\Rightarrow \theta=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\frac{\pi}{6}$

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