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The sine of the angle between the pair of lines represented by the equation \(x^2-7 x y+12 y^2=0\) is
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2403 Upvotes
Verified Answer
The correct answer is:
\(\frac{1}{\sqrt{170}}\)
\(\begin{aligned}
& x^2-7 x y+12 y^2 =0 \\
a & =1(2 h=-7) b=12 \\
\tan \theta & =\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \\
& =\left|\frac{2 \sqrt{\frac{49}{4}-1 \cdot 12}}{13}\right|=\left|\frac{2 \cdot \frac{1}{2}}{13}\right|
\end{aligned}\)
\(\tan \theta=\frac{1}{13}\)
\(\sin \theta=\frac{1}{\sqrt{170}}\)
Hence, option (c) is correct.
& 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.
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