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Question: Answered & Verified by Expert
If $\theta$ is an acute angle between the lines $k x^2-4 x y+y^2=0$ and $\tan \theta=\frac{1}{2}$, then value of $k$ is
MathematicsPair of LinesMHT CETMHT CET 2022 (10 Aug Shift 2)
Options:
  • A $21$
  • B 4
  • C 3
  • D $-3$
Solution:
1612 Upvotes Verified Answer
The correct answer is: 3
$\begin{aligned} & \tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \\ & \Rightarrow \frac{1}{2}=\left|\frac{2 \sqrt{(-2)^2-k \times 1}}{k+1}\right| \\ & \Rightarrow \pm \frac{1}{2}=\frac{2 \sqrt{4-k}}{k+1} \\ & \Rightarrow \pm(k+1)=4 \sqrt{4-k} \\ & \Rightarrow k=3\end{aligned}$

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