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

• A

  \(\frac{1}{12}\)
• B

  \(\frac{1}{13}\)
• Correct answer
  C

  \(\frac{1}{\sqrt{170}}\)
• D

  \(\frac{1}{11}\)

Solution

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

Hence, the correct answer is option: 'C'.