Conic Sections

The general equation of a conic section is

In the problems that we have been looking at, E=0. In this case the axes of the conic section are horizontal and/or vertical. The graph can be determined by ``completing the squares'' of the x and y. The graph may be degenerate (empty, a single point, a line, or a pair of crossing lines). If the graph is not degenerate, then we can tell what curve we will have:

• A=B: circle.
• but A and B have the same sign: ellipse.
• A and B have opposite signs: hyperbola.
• A=0 or B=0 (but not both): parabola.