find the airthmatic mean of the oordinate of feet of normals from the point (3,5) to the parabola  y² = 8x

Parametric equation of normal : y = tx - 2at - at³

y = tx - 4t - 2t³

It oasses through (3,5)

5 = 3t - 4t - 2t³

2t³ + t + 5 = 0

If its roots are p,q,r then p+q+r = 0

Oridnates of feets of normals are given by 2ap,2aq,2ar i.e. 4p,4q,4r

their arithmetic mean = (4p+4q+4r)/3 = (4/3)(o+q+r) = 0