Equation of tangent at point P(2,4) to parabola y2=8x is
4y=4(x+2)⇒4x−4y+8=0⋯(1)
Let (x1,y1) be the mid point of the chord QR
Equaion of chord of the parabola y2=8x+5 whose mid point is (x1,y1) will be
T=S1⇒yy1−4(x+x1)−5=y21−8x1−5⇒4x−yy1+y21−4x1=0⋯(2)
∵ Both equation (1) and (2) represents the same equation
Hence, comparing (1) and (2), we get
44=y14=y21−4x18
⇒y1=4
⇒x1=2
∴The required sum is 4+2=6