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
$x^2-5xy+4y^2+3x-4=0$
$\therefore \tan \theta =\left|\frac{2\sqrt{{\left(-\frac{5}{2}\right)}^2-4}}{5}\right|$
$=\left|\frac{2\sqrt{\frac{25}{4}-4}}{5}\right|=\frac{2}{5}\times \sqrt{\frac{9}{4}}=\frac{2}{5}\times \frac{3}{2}=\frac{3}{5}$
$\Rightarrow {\tan }^2\theta =\frac{9}{25}$