Question

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

• A. $\frac{1}{12}$
• B. $\frac{1}{13}$
• C. $\frac{1}{\sqrt{170}}$
• D. none of these

Answer 1

Answer: (C)

$\frac{1}{\sqrt{170}}$

We know that the equation $a{x}^2+2hxy+b{y}^2=0$ represents a pair of straight lines passing through origin.The sine of angle between these lines is given by $\frac{2\sqrt{h^2-ab}}{\sqrt{(a-b{)}^2+4h^2}}$.
Here $a=1,b=12,h=-\frac{7}{2}$.

Let the angle between the lines is $\alpha$
$\Rightarrow \sin \alpha =\frac{2\sqrt{(\frac{-7}{2}{)}^2-12}}{\sqrt{(1-12{)}^2+4(\frac{-7}{2}{)}^2}}=\frac{1}{\sqrt{170}}$