AP EAMCET · Maths · Pair of Lines
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 \(\frac{1}{13}\)
- C \(\frac{1}{\sqrt{170}}\)
- D \(\frac{1}{11}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{170}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & x^2-7 x y+12 y^2 =0 \\ a & =1(2 h=-7) b=12 \\ \tan \theta & =\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \\ & =\left|\frac{2 \sqrt{\frac{49}{4}-1 \cdot 12}}{13}\right|=\left|\frac{2 \cdot \frac{1}{2}}{13}\right| \end{aligned}\) \(\tan \theta=\frac{1}{13}\)…
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