The acute angle between the lines represented by 6 x^2-x y-y^2=0 … - Vidyadip

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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