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JEE Main202523 Jan 2025Evening ShiftMathematicsParabolaActual

The focus of the parabola y^2=4 x+16 is the centre of the circle C of radius 5 . If the values of , for which C passes through the point of intersection of the lines 3 x-y=0 and x+ y=4 , are ₁ and ₂, ₁ ₂ , then 12 ₁+29 ₂ is equal to

Correct answer

0

Step-by-step solution

y^2=4(x+4) Equation of circle (x+3)^2+y^2=25 Passes through the point of intersection of two lines 3 x-y=0 and x+ y=4 ( 4 3 +1 , 12 3 +1 ) , we get aligned & =- 7 6 , 1 & 12 ₁+29 ₂ & -14+29=15 aligned

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