JEE Mains · Maths · STD 11 - 9. straight line
Let the angles made with the positive x-axis by two straight lines drawn from the point \( P(2,3) \) and meeting the line \( x+y=6 \) at a distance \( \sqrt{\frac{2}{3}} \) from the point P be \( \theta_{1} \) and \( \theta_{2} \). Then the value of \( (\theta_{1}+\theta_{2}) \) is:
- A \( \frac{\pi}{12} \)
- B \( \frac{\pi}{6} \)
- C \( \frac{\pi}{2} \)
- D \( \frac{\pi}{3} \)
Answer & Solution
Correct Answer
(C) \( \frac{\pi}{2} \)
Step-by-step Solution
Detailed explanation
Let Q is \( (\sqrt{\frac{2}{3}}\cos\theta+2, \sqrt{\frac{2}{3}}\sin\theta+3) \) so, \(x+y=6\) \( \sqrt{\frac{2}{3}}(\cos\theta+\sin\theta)+5=6 \) \( \sin\theta+\cos\theta=\sqrt{\frac{3}{2}} \) \(1+\sin 2 \theta=\frac{3}{2}\) \(\sin 2 \theta=\frac{1}{2}\)…
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