Question

The angle between the lines $x^2-xy-6y^2-7x+31y-18=0$ is

• A. ${60}^o$
• B. ${45}^o$
• C. ${30}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${45}^o$

In the equation of pair of straight lines $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0,$ the angle between the lines is $\theta$ and $\tan \left(\theta \right)=\frac{2\sqrt{h^2-ab}}{a+b}$

Here, $a=1,b=-6,h=\frac{-1}{2}$

$\therefore \tan \left(\theta \right)=\frac{2\times \sqrt{\frac{1}{4}+6}}{1-6}$

$=\pm \frac{2\times \frac{5}{2}}{-5}$

$=\pm 1$

$\therefore \theta ={45}^o$ either in the clockwise or anticlockwise sense.