Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
The angle between the lines represented by $\sqrt{3} x y-y^2=0$ is
A
$30^{\circ}$
B
$45^{\circ}$
✓
$60^{\circ}$
D
$90^{\circ}$
✓
Answer
Correct option: C.
$60^{\circ}$
(C) Given equation of pair of lines is $\sqrt{3} x y-y^2=0$ $\therefore \quad a =0, h=\frac{\sqrt{3}}{2}, b=-1$ $\therefore \quad \tan \theta=\left|\frac{2 \sqrt{\frac{3}{4}-0}}{0-1}\right|=\left|\frac{2 \times \frac{\sqrt{3}}{2}}{-1}\right|=\sqrt{3}$ $\Rightarrow \theta=\tan ^{-1}(\sqrt{3})=60^{\circ}$
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