TS EAMCET · Maths · Straight Lines
Let the angle between the lines \(x-2 y+3=0\) and \(k x-y+2=0\) be \(45^{\circ}\). If \(k_1, k_2\left(k_1>k_2\right)\) are two distinct real values of \(k\), then \(k_1-2=\)
- A \(\mathrm{k}_2\)
- B \(-\mathrm{k}_2\)
- C \(-3 \mathrm{k}_2\)
- D \(3 \mathrm{k}_2\)
Answer & Solution
Correct Answer
(C) \(-3 \mathrm{k}_2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \tan 45^{\circ}=\left|\frac{\frac{1}{2}-k}{1+\frac{k}{2}}\right| \\ & \Rightarrow \quad\left|\frac{1}{2}-k\right|=\left|1+\frac{k}{2}\right| \\ & \Rightarrow \quad|1-2 k|=|2+k| \\ & \therefore \quad 1-2 k= \pm(k+2) \\ & \quad 1-2 k=k+2 \text { or } 1-2…
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