The relativistic cyclotron resonance condition for right-handed extraordinary mode waves defines an ellipse in velocity space. The position of the center and size of the semiminor axis of this ellipse are functions of the plasma frequency, gyrofrequency, wave frequency, and wave normal angle. The effect of varying these parameters on the position and size of the resonance contour is analyzed. The results show that as the wave normal angle decreases, the semiminor axis increases in size and as the plasma frequency to gyrofrequency ratio decreases, the minimum energy for resonating electrons decreases and the maximum wave normal angle allowed by the resonance condition increases. Also, as the wave frequency to gyrofrequency ratio increases, the center of the resonance ellipse moves away from the origin. The relativistic resonance condition and the electron distribution in velocity space obtained by the S3-3 satellite are used to calculate numerically growth rates for the terrestrial auroral kilometric radiation. It is shown that the loss cone region of the electron distribution can give rise to growth rates for the extraordinary mode that are sufficiently large to account for the observed radio emission intensities.