Given, equation of parabola is y2=8x ...(i) ∴a=2
Let (h,4) be the coordinate of mid-point of chord.
Then, equation of chord is y−4=m(x−h) ...(ii)
If line (ii) passes through the point P(2t12,4t1) and Q(2t22,4t2) on parabola Eq. (i), then y(t1+t2)−2x−4t1t2=0 ...(iii)
having slope m=t1+t22 ...(iv)
Since, (h,4) is the mid-point of PQ. Therefore, 2×4=4(t1+t2) ⇒t1+t2=2
Hence, slope of chord PQ is m=22=1 [using Eq. (iv)]