If an electron has an initial velocity in a direction different from that of an electric field the path of the electron is

Let electric filed is along x axis and initial velocity of the electron be v which makes angle θ with x axis.

So initial velocity of electron along x axis v_x = v cosθ and acclaration along x is a = -eE/m . (e = charge of electrn, m= mass of electron and E = magnitude of electric filed intensity). And intitial velocity along y direction is v_y = v sinθ, as there is on force electron along y direction so v_y remains unchanged with time.

At any time t let the electron be at (x,y) position (assuming it starts from origin).

Hence x = (v cosθ)t - 0.5(eE/m)t^2     and y = (v sinθ)t