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Pair of Straight Lines — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
The angle between the lines represented by the equation $\left(x^2+y^2\right) \sin \theta+2 x y=0$ is
  • A
    $\theta$
  • B
    $\frac{\theta}{2}$
  • ✓
    $\frac{\pi}{2}-\theta$
  • D
    $\frac{\pi}{2}-\frac{\theta}{2}$
✓

Answer

Correct option: C.
$\frac{\pi}{2}-\theta$
(C) Given equation of pair of lines is $\left(x^2+y^2\right) \sin \theta+2 x y=0$
$\therefore \quad a=b=\sin \theta, h=1$
$\therefore \quad \tan \theta=\left(\frac{2 \sqrt{1-\sin ^2 \theta}}{2 \sin \theta}\right)$
$\Rightarrow \theta=\tan ^{-1}\left(\frac{\cos \theta}{\sin \theta}\right)=\tan ^{-1}(\cot \theta)$
$\Rightarrow \theta=\tan ^{-1}\left\{\tan \left(\frac{\pi}{2}-\theta\right)\right\}=\frac{\pi}{2}-\theta$

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