A line passing through the point P(a, θ) makes an acute angle α with the positive x-axis. Let this line be rotated about the point P through an angle (α)/2 in the clockwise direction. If in the new position, the slope of the line is 2 - √(3) and its distance from the origin is 1/(√(2)), then the value of 3a² tan ² α - 2√(3) is:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q212

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

A line passing through the point

P(a, \theta)

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 clockwise 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

3a^2 \tan^2 \alpha - 2\sqrt{3}

is:

JEE Main 2025 Coordinate Geometry Question with Solution (April Unspecified (session-level dataset), Q212) | JEE Arc