Reduced Equation of a Conic

By making the right choice of orthonormal frame, the equation of the non-degenerate conic can be simplified to one of the following reduced equations, given and illustrated below:

An ellipse:

A hyperbola (first possibility):

A hyperbola (second possibility):

A parabola (first possibility):

A parabola (second possibility):

For sake of completeness, we mention that the second possibility of the hyperbola and the parabola are contained in the first possibility. One only has to switch the role of x and y, which corresponds to a reflection with respect to the first bisector. VisuMath, however, works with the five given forms.

VisuMath will calculate the general equation of the conic and make a drawing of it in which all relevant axes are also drawn. First one chooses the right type of conics and enters the appropriate values of the parameters.