A hyperbola comprises two disconnected curves called its arms which separate the foci. At large distances from the foci the hyperbola begins to approximate two lines, known as asymptotes.
A hyperbola has the property that a ray originating at one of the foci is reflected in such a way as to appear to have originated at the other focus.
A special case of the hyperbola is the rectangular hyperbola, in which the asymptotes intersect at right angles. The rectangular hyperbola with the coordinate axes as its asymptotes is given by the equation xy=c, where c is a constant.
Just as the equation of the ellipse in parametric form is related to the sine and cosine functions, so the equation of the hyperbola in parametric form is related to the hyperbolic sine and hyperbolic cosine.
A body that has sufficient energy to escape the gravitational field of a massive body moves in a hyperbolic trajectory with the massive body at one of the foci.
Equations (Cartesian):
Equations (Polar):
Equations (Parametric):
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