Question

Find the angle between the pair of straight lines $4x^2+24xy+11y^2=0$

Answer 1

Given equation is $4x^2+24xy+11y^2=0$
Here a = coeff of $x^2=4$, b = coeff of $y^2=11$ and $2h=$ coeff of xy $=24$
$\therefore h=12$
Now $\tan \theta =\left|\frac{2\sqrt{h^2-ab}}{a+b}\right|=\left|\frac{2\sqrt{144-44}}{4+11}\right|=\frac{4}{3}$
Where $\theta$ is the acute angle between the lines
$\therefore$ acute angle between the lines is ${\tan }^{-1}\left(\frac{4}{3}\right)$ and obtuse angle between them is $\pi -{\tan }^{-1}\left(\frac{4}{3}\right)$