Conics: eccentricity and directrices
In this figure, drag a focus and a vertex to create ellipses and hyperbolas.
is the center-to-focus distance.
is the center-to-vertex distance.
The eccentricity of an ellipse or a hyperbola is defined as .
The equation describes both ellipses and hyperbolas in the Cartesian plane centered at the origin with foci on the -axis. The shape is an ellipse if and the shape is a hyperbola if .
The directrices of ellipses and hyperbolas are lines perpendicular to the focal axis, a distance from the origin.
The focus-directrix equation states that for all conics. See if you can demonstrate this equation with the interactive figure here.
This applet was developed for use with Interactive Calculus, published by Pearson.