How To Identify Conic Sections

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.

How to identify conic sections. In the formula a b c d e and f are all constants. An extreme point on a conic section. We get circles when we cut our cone straight across.

When either x or y is squared not both. For example take a look at 3 x 2 12 x. By changing the angle and location of the intersection we can produce different types of conics.

The procedure to locate the intersection points follows these steps where the conics are represented by matrices. A straight line which a curve approaches arbitrarily closely as it goes to infinity. This general form covers all four unique flat shapes.

When a conic is written in the form ax 2 by 2 cx dy e 0 then the following rules can be used to determine what type of relation it is. Given the two conics c 1 displaystyle c 1 and c 2 displaystyle c 2 consider the pencil of conics given by. There are several ways of classifying conic sections using the above general equation with the help of the discriminant.

F x y ax2 2hxy by2 2gx 2f y c 0. The equations y x 2 4 and x 2 y 2 3. A point used to construct and define a conic.

The set of all points whose coordinates satisfy a given equation or condition. Circles ellipses hyperbolas and parabolas. How to identify a conic section by its formulas a conic section.