jee-main 2025 Q19

jee-main · India · session1_24jan_shift2 Conic sections Equation Determination from Geometric Conditions
If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x + 2y = 0$ is $\alpha x^{2} + \beta y^{2} - \gamma xy - 30x - 60y + 225 = 0$, then $\alpha + \beta + \gamma$ is equal to:
(1) 7
(2) 9
(3) 8
(4) 6
If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x + 2y = 0$ is $\alpha x^{2} + \beta y^{2} - \gamma xy - 30x - 60y + 225 = 0$, then $\alpha + \beta + \gamma$ is equal to:\\
(1) 7\\
(2) 9\\
(3) 8\\
(4) 6