Parabola
Parabola
nta_pyq_2025_jan
Grade 11
Question:
If the equation of the parabola with vertex V ( 3 , 3) and the directrix x + 2y = 0 is 2 \alphax 2 + \betay 2 - \gammaxy - 30x - 60y + 225 = 0 , then \alpha + \beta + \gamma is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
(2) \therefore Equation of parabola is P S = (1)P M 2 2 \Rightarrow PS = PM 2 x + 2y 2 2 (x - 3) + (y - 6) = ( ) \sqrt5 2 2 2 2 5x - 30x + 5y - 60y + 225 = x + 4y + 4xy 2 2 4x + y - 4xy - 30x - 60y + 225 = 0 We get : \alpha = 4, \beta = 1, \gamma = 4 \therefore \alpha + \beta + \gamma = 9
Correct Answer: 2