If the equation of the parabola with vertex V(3/2, 3) and the directrix x + 2y = 0 is α x² + β y² - γ xy - 30x - 60y + 225 = 0, then α + β + γ is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q194

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

If the equation of the parabola with vertex

\mathbf{V}\left(\frac{3}{2}, 3\right)

and the directrix

x + 2y = 0

\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0

, then

\alpha + \beta + \gamma

is equal to: