JEE Mains · Maths · STD 11 - 9. straight line
A line passing through the point \(\mathrm{P}(\mathrm{a}, 0)\) makes an acute angle \(\alpha\) with the positive x -axis. Let this line be rotated about the point \(P\) through an angle \(\frac{\alpha}{2}\) in the clock-wise direction. If in the new position, the slope of the line is \(2-\sqrt{3}\) and its distance from the origin is \(\frac{1}{\sqrt{2}}\), then the value of \(3 a^2 \tan ^2 \alpha-2 \sqrt{3}\) is
- A 4
- B 6
- C 5
- D 8
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{m}_{\mathrm{PR}}=2-\sqrt{3}=\tan 15^{\circ} \\ & \therefore \frac{\alpha}{2}=15^{\circ} \quad \Rightarrow \alpha=30^{\circ} \end{aligned}\) equation of PR : \(\begin{aligned} & y=\tan 15^{\circ}(x-a) \\ & y=(2-\sqrt{3})(x-a) \end{aligned}\) \(\perp\)…
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