Search any question & find its solution
Question:
Answered & Verified by Expert
If $\theta$ is the acute angle between the pair of lines $12 x^2+2 h x y+7 y^2=0$ and $\tan \theta=\frac{8}{19}$, then $h=$
Options:
Solution:
1178 Upvotes
Verified Answer
The correct answer is:
\pm 10
$\because \quad$ Angle between the pair of lines is defined by
$$
\begin{aligned}
& \tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \\
& \Rightarrow \frac{8}{19}=\frac{2 \sqrt{h^2-12 \times 7}}{12+7} \\
& \Rightarrow 4=\sqrt{h^2-84} \\
& \Rightarrow 16=h^2-84 \\
& \Rightarrow h^2=100 \Rightarrow h= \pm 10
\end{aligned}
$$
$$
\begin{aligned}
& \tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \\
& \Rightarrow \frac{8}{19}=\frac{2 \sqrt{h^2-12 \times 7}}{12+7} \\
& \Rightarrow 4=\sqrt{h^2-84} \\
& \Rightarrow 16=h^2-84 \\
& \Rightarrow h^2=100 \Rightarrow h= \pm 10
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.