Question

If $\theta$ is the angle between the pair of straight lines $x^2 - 5xy + 4y^2 + 3x - 4 = 0$, then $\tan^{2}\theta$ is equal to

• A. $\frac{9}{16}$
• B. $\frac{16}{25}$
• C. $\frac{9}{25}$
• D. $\frac{21}{25}$
• E. $\frac{25}{9}$

Answer 1

Answer: (C)

Given equation of straight line is
$x^{2}-5 x y+4 y^{2}+3 x-4=0$
$\therefore \tan \theta=\left|\frac{2 \sqrt{\left(-\frac{5}{2}\right)^{2}-4}}{5}\right|$
$=\left|\frac{2 \sqrt{\frac{25}{4}-4}}{5}\right|=\frac{2}{5} \times \sqrt{\frac{9}{4}}=\frac{2}{5} \times \frac{3}{2}=\frac{3}{5}$
$\Rightarrow \,\tan ^{2} \theta=\frac{9}{25}$