Question

The angle between the lines $2x^2-7xy+3y^2=0$ is

• A. ${60}^0$
• B. ${45}^0$
• C. ${\tan }^{-1}\left(\frac{7}{6}\right)$
• D. ${30}^0$

Answer 1

The correct option is B ${45}^0$

Here $a=2,b=3,h=-\frac{7}{2}$

If $\theta$ is the angle between the lines, then

$tan\theta =\frac{2\sqrt{h^2-ab}}{a+b}=\frac{2\sqrt{\frac{49}{4}-6}}{2+3}=1\Rightarrow \theta =\frac{\pi }{4}$