The sine of the angle between the pair of lines represented by the equation $x^2-7 x y+12 y^2=0$ is

Question

Aicharya · Accepted Answer

$\begin{aligned} & x^2-7 x y+12 y^2 =0 \ a & =1(2 h=-7) b=12 \ \tan \theta & =\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \ & =\left|\frac{2 \sqrt{\frac{49}{4}-1 \cdot 12}}{13}\right|=\left|\frac{2 \cdot \frac{1}{2}}{13}\right| \end{aligned}$ $\tan \theta=\frac{1}{13}$ $\sin \theta=\frac{1}{\sqrt{170}}$ Hence, option (c) is correct.

The sine of the angle between the pair of lines represented by the equation \(x^2-7 x y+12 y^2=0\) is

Solution