What happens to the shape of an orbit as eccentricity gets larger?

As the eccentricity of an orbit increases, the shape of the orbit becomes more elongated or stretched. An eccentricity of 0 corresponds to a perfect circle, while values between 0 and 1 indicate elliptical orbits. As eccentricity approaches 1, the orbit becomes increasingly elongated, resembling a parabola when it reaches 1, and transitioning to a hyperbolic shape for values greater than 1. Thus, higher eccentricity results in a more elongated and less circular orbit.