The standard constants in an ellipse and a hyperbola are h, k, a, b, and c. The center is at (h, k). The distance from the center to a vertex is a, and the distance from the center to a focal point is c. The sum constant for an ellipse is 2a and the difference constant for a hyperbola is also 2a.
The standard equations are:
depending on the orientation of the conic and the type of conic and on how you want t to traverse the conic. In all of the parametric equations above, I am letting t go from 0 to 2π. This is just a sampling of the possibilites since there are many ways you can make t traverse the conic. You can experiment in your graphing calculator, by hand, or by using an interactive program with these equations.
horizontally orientated ellipse:
which is equivalent to
or
vertically orientated ellipse:
which is equivalent to
or
horizontally orientated hyperbola:
which is equivalent to
vertically orientated hyperbola
which is equivalent to
Page Updated: April 8, 2010
