Verified Solution • 2025–26 Session moderate

QJEEM25Ma6345: JEE Main 2025 Mathematics - Class 11 JEEM25Ma6345 Solution: If the equation of the parabola with vertex and the directrix…

If the equation of the parabola with vertex V(32,3)\mathrm{V}\left(\frac{3}{2}, 3\right) and the directrix x+2y=0x+2 y=0 is αx2+βy2−γxy−30x−60y+225=0\alpha x^2+\beta y^2-\gamma x y-30 x-60 y+225=0 , then α+β+γ\alpha+\beta+\gamma is equal to :

Multiple Choice Options

  • A 6
  • B 8
  • C 7
  • D 9

Step-by-Step Verified Solution

Equation of axis

y−3=2(x−32)y−2x=0

foot of directrix

y−2x=0&⇒(0,0)2y+x=0

 Focus =(3,6)PS2=P2(x−3)2+(y−6)2=(x+2y5)24x2+y2−4xy−30x−60y+225=0⇒α=4,β=1,γ=4⇒α+β+γ=9

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