- the two green
curves together are a hyperbola
- The point k is defined so that the distance between k and
f is exactly twice the distance between k
and the red line
- the point f
is a focus of the hyperbola, and the red line is a directrix of the
hyperbola.
- a hyperbola actually has two focus
points and two directrix lines. The hyperbola shown has another focus at
(-4,0), and another directrix at x = -1
- for all hyperbolas, the distance
between k and the focus is a constant
multiple of the distance between k and the directrix. This constant multiple is
called the eccentricity of the hyperbola. The hyperbola shown above has
an eccentricity of 2
- all hyperbolas have an eccentricity
greater than 1
- Typically, a hyperbola has
equation:
- Its eccentricity, e, is found from:
- The directrices are at:
- The foci are at (±ae,0)
- The asymptotes are
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