A line passing through the point P(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 {1}/{\sqrt{2}}, then the value of 3 a^2 \tan ^2 \alpha-2 \sqrt{3} is [8 Apr 2025 Shift 2]

Straight Lines and Pair of Straight Lines Part 2

Section: Mathematics

Question : 9 of 72

Marks: +1, -0

A line passing through the point P(a,0) makes an acute angle α with the positive x-axis. Let this line be rotated about the point P through an angle ‌

in the clock-wise direction. If in the new position, the slope of the line is 2−√3 and its distance from the origin is ‌

√2

, then the value of 3a2tan2α−2√3 is

[8 Apr 2025 Shift 2]

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