- the green
curve is an ellipse
- the position of the point k has
the property that the distance between k and f
is exactly half of the distance between k and the
red line.
- the point f
is called a focus of the ellipse, and the
red line is called a directrix of the
ellipse.
- an ellipse actually has two focus
points and two directrix lines. The ellipse shown above has another focus at
(-1,0), and another directrix at x = -4, which are mirror-symmetric to the ones
displayed
- an ellipse does not have a "radius"
like a circle does. Observe that the points on the ellipse are located at
different distances from the ellipse's center at the origin
- the maximum of these distances is
called the semimajor axis and the minimum of these distances is called
the semiminor axis
- the ellipse shown has a semimajor axis
= 2, and a semiminor axis = V¯3. For all ellipses, the distance between k
and the focus is a constant fraction of the distance between k and the
directrix
- this constant fraction is called the
eccentricity of the ellipse. The ellipse shown has an eccentricity of
0.5.
- all ellipses have an eccentricity
between 0 and 1
- Typically, an ellipse has
equation:
- Its eccentricity, e, is found from:
- The directrices are at:
- The foci are at (±ae,0)
|
The