TS EAMCET · Maths · Straight Lines
Two lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\) passing through the point \(\mathrm{P}(1,2)\) cut the line \(x+y=4\) at a distance of \(\frac{\sqrt{6}}{3}\) units from \(P\). Then the angles made by \(\mathrm{L}_1, \mathrm{~L}_2\) with positive \(\mathrm{X}\)-axis are
- A \(\frac{\pi}{3}, \frac{\pi}{6}\)
- B \(\frac{\pi}{8}, \frac{3 \pi}{8}\)
- C \(\frac{\pi}{12}, \frac{5 \pi}{12}\)
- D \(\frac{\pi}{4}, \frac{\pi}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{3}, \frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\[ P(1,2), r=\frac{\sqrt{6}}{3} \] Let \(L_1\) and \(L_2\) cut the line \(x+y=4\) at \(\left(x_1, y_1\right)\) By parametric form \[ x_1=1+\sqrt{\frac{6}{3}} \cos \theta, y_1=2+\sqrt{\frac{6}{3}} \sin \theta \]…
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