How To Graph Conic Sections

The graphic below shows how intersections of a two napped cone and a plane form a parabola ellipse circle and a hyperbola.

How to graph conic sections. When graphing conic sections in polar form you can plug in various values of theta to get the graph of the curve. X 2 a 2 y 2 b 2 1. A conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane.

When a plane intersects a two napped cone conic sections are formed. Given a general form conic equation in the form ax 2 cy 2 dx ey f 0 or after rearranging to put the equation in this form that is after moving all the terms to one side of the equals sign this is the sequence of tests you should keep in mind. If neither x nor y is squared then the equation is that of a line.

If e 0 the conic section is a circle. Certain characteristics are unique to each type of conic and hint to you which of the conic sections you re graphing. When placed like this on an x y graph the equation for an ellipse is.

It explains how to graph parabolas in standard form and how to g. The three types are parabolas ellipses and hyperbolas. We can make an equation that covers all these curves.

The variable e determines the conic section. This algebra video tutorial provides a basic introduction into parabolas and conic sections. Every conic section has certain features including at least one focus and directrix.

A conic section can be graphed on a coordinate plane. A conic section is a special class of curves. The special case of a circle where radius a b.