Скачать или смотреть What is Eccentricity? (Conic Sections)

This animation, created using MATLAB, illustrates the eccentricity (e) of a conic section. It can be perceived as a measure of the conic's flatness or skewness.

In the case of an ellipse, e equals 0 corresponds to a circle (which is not skewed at all). As e increases towards 1, the ellipse appears to be more of a football than a circle. That is, its major semiaxis grows faster than its minor semiaxis.

When e equals 1, the intersecting plane is slanted in the same direction as the cone itself, which forms a parabola.

When e surpasses 1, the conic is an hyperbola with a large gap between the branches. As e continues to increase, the gap shortens and the hyperbola itself appears to be skewed near its center. As e approaches infinity, the hyperbola approaches its asymptotes, which are the black dotted lines.

It should be noted that the skewness for the hyperbola is exaggerated in this video since the actual conic section is the curve in space projected "down" onto the xy axis.