Maharashtra BoardEnglish MediumSTD 12 ScienceMathsPair of Straight Lines2 Marks
MCQ
The acute angle between the lines represented by $6 x^2-x y-y^2=0$ is
✓
$45^{\circ}$
B
$30^{\circ}$
C
$60^{\circ}$
D
$90^{\circ}$
✓
Answer
Correct option: A.
$45^{\circ}$
(A) Given equation of pair of lines is $6 x^2-x y-y^2=0$ $\therefore \quad a =6, h=-\frac{1}{2}, b=-1$ If $\theta$ is the acute angle between the pair of lines, then $\tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|$ $\begin{array}{l}\Rightarrow \tan \theta=\left|\frac{2 \sqrt{\frac{1}{4}+6}}{5}\right|=1 \\ \Rightarrow \theta=\tan ^{-1}(1)=45^{\circ}\end{array}$
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