## Analytic Geometry: The Hyperbola

[caption id="attachment_6399" align="alignright" width="380"] Simple hyperbola with asymptotes. Image by author.[/caption] The parabola, ellipse, circle, and hyperbola are all termed conic sections. This means that a plane that cuts into a cone in just the right way will generate one of these figures. We will consider the basic equation of a hyperbola and graph one. Equation of an Hyperbola It may be recalled the equation for an ellipse centered at the origin is, x2/a2 + y2/b2 = 1 where 2a is the length of the ellipse and 2b is its height. The equation for an hyperbola centered at the origin is very similar, x2/a2 - y2/b2 = 1 The graph of this function is completely different from that of an ellipse. Let's look at a very basic one, for which…