The electron has an initial velocity along the x-direction $(v_x = v_0).$The electric field is applied along the y-direction $(E_y = E_0).$The force acting on the electron is $\vec{F}= -e \vec{E}= -e E_o \hat{j}$.This produces a constant acceleration in the y-direction $\left(a_y=-\frac{eE_0}{m}\right)$, while the velocity along x remains unchanged.Since $x = v_o t$ and $y = \frac{1}{2} a_y t^2$, eliminating time gives $y \propto x^2$, which represents a parabolic trajectory.The electron follows a parabolic path.