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JEE Main202528 Jan 2025Evening ShiftMathematicsParabolaActual

Let A and B be the two points of intersection of the line y+5=0 and the mirror image of the parabola y^2=4 x with respect to the line x+y+4=0 . If d denotes the distance between A and B , and a denotes the area of S A B , where S is the focus of the parabola y^2=4 x , then the value of (a+d) is -

Correct answer

0

Step-by-step solution

To find image of P (t^2, 2 t ) aligned & x-t^2 1 = y-2 t 1 = -2 (t^2+2 t+4 ) 1^2+1^2 =-(t+1)^2-3 & x=t^2-(t+1)^2-3=-2 t-4 & y=2 t-(t+1)^2-3=-t^2-4 & t= -x-4 2 & y+4=- ( -x-4 2 )^2 & (y+4)=- (x+4)^2 4 & x^2=-4 y & Focus (-4,-5) aligned Also, y=-5 intersect aligned & (-4)(-1)=(x+4)^2 & 4=(x+4)^2 & x+4= 2 & x=-2,-6 & d=4 & a= 1 2 | array ccc 1 & 0 & 1 -2 & -5 & 1 -6 & -5 & 1 array | & = 1 2 |[1(-5+5)+1(10-30)]| & = 1 2 (20) & a=10 & a+d=14 aligned

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