In the current article, the binding energy and impurity-related photoionization cross-section are investigated for the case of an infinite confinement potential well model using a variational approach for hydrogen-like impurity states in strongly prolate ellipsoidal quantum dot. The binding energy is calculated as a function of ellipsoidal small and large semiaxes and as a function of impurity displacement. The behavior of the oscillator strength for the quantum transitions between the impurity ground state and the first two non-impurity states are considered for different values of incident light angles and geometrical parameters. In the work, we illustrate the results of photoionization cross-section computations depending on the incident photon energy for a range of incident angles and different values of impurity shift. It is revealed that the threshold frequency decreases with the increase of impurity displacement.