If for θ [ -(π)/3, 0 ], the points (x, y) = (3 tan (θ + (π)/3), 2 tan (θ + (π)/6)) lie on xy + α x + β y + γ = 0, then α² + β² + γ² is equal to:

Trigonometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q183

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumTrigonometry118× since 2002

If for

\theta \in \left[ -\frac{\pi}{3}, 0 \right]

, the points

(x, y) = \left( 3 \tan\left(\theta + \frac{\pi}{3}\right), 2 \tan\left(\theta + \frac{\pi}{6}\right) \right)

lie on

xy + \alpha x + \beta y + \gamma = 0

, then

\alpha^2 + \beta^2 + \gamma^2

is equal to:

JEE Main 2025 Trigonometry Question with Solution (April Unspecified (session-level dataset), Q183) | JEE Arc