The first person to describe conic sections in the formal language of
Euclid's geometry, as well as coining the names
of three of the conic sections, was the ancient
Greek mathematician Appolonius of Perga. The four conic sections
are the *circle*, the *ellipse*, the *parabola*,
and the *hyperbola* (the last three names being the ones coined
by Appolonius). They are called *conic sections* because they are
the shapes formed by the intersection of a plane with a conical surface.
As well, the general class of conic sections also includes as special cases
a point (at the cone's apex) and pairs of straight lines (degenerate
hyperbolas passing through the apex of the cone). The type of conic
section produced by this intersection depends on the angle at which the
plane intersects the cone's surface.

A circle is defined as the set of points that are equidistant from a
point. A variation of this would be to find all points for which the
distance from that point to a reference point is equal to the distance
from that point to a line multiplied by a constant. This technique is
so important that special names are used for the line, the point, and the
constant. The point is the focus. The line is called the directrix.
The constant, which is defined as the ratio of the distance from the
focus to the distance from the directrix is the eccentricity, which is
abbreviated as `e`.

A circle is defined to have eccentricity 0. Every eccentricity
between (but not including) 0 and 1 is an ellipse. If `e` = 1,
the curve produced is a parabola. Every point on a parabola is
equidistant from the focus and the directrix. Unlike an ellipse,
notice that a parabola is not a closed curve. Curves with eccentricity
greater than 1 are called hyperbolas. Notice that they include points
on both sides of the directrix.

Also, a conic section is produced when an equation of the second degree is graphed. An equation of the second degree is one of the form

where `a` through `f` are constants. For example:

- A circle is obtained when
`b`= 0 and`a`=`c`. - An ellipse whose axes are aligned with the axes of the graph is produced when
`b`= 0 and`a`⁄`c`is positive and not equal to 1. - A parabola is obtained when
`b`= 0 and one of`a`or`c`is equal to 0. - A hyperbola whose axes are aligned with the axes of the graph is produced when
`b`= 0 and`a`⁄`c`is negative.