JEE Main202524 Jan 2025Evening ShiftMathematicsParabolaActual

If the equation of the parabola with vertex V ( 3 2 , 3 ) and the directrix x+2 y=0 is x^2+ y^2- x y-30 x-60 y+225=0 , then + + is equal to :

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Correct answer

B. 9

Step-by-step solution

aligned & Equation of parabola is P S=(1) P M & P S^2=P M^2 & (x-3)^2+(y-6)^2= ( x+2 y 5 )^2 & 5 x^2-30 x+5 y^2-60 y+225=x^2+4 y^2+4 x y & 4 x^2+y^2-4 x y-30 x-60 y+225=0 aligned We get : =4, =1, =4 + + =9

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