Terms
Axis

The line over which a parabola is symmetric.
Branch

The term for each of the two distinct sections of the graph of a hyperbola.
Center

For an ellipse and hyperbola, the midpoint between the foci. For a
circle, the fixed point from which all points on the circle are equidistant.
Circle

The set of all points equidistant from a given fixed point.
Conic

The intersection of a plane and a right circular cone.
Conjugate Axis

The line segment related to a hyperbola of length
2b
whose midpoint is the
center.
Degenerate Conic

A conic which is not a parabola, ellipse, circle, or
hyperbola. These include lines, intersecting lines, and points.
Diameter

A line segment that contains the center of a circle whose endpoints are
both on the circle, or sometimes, the length of that segment.
Directrix

For a parabola, it is the line whose distance from any point on the parabola
is the same as the distance from that point to the focus. For a conic
defined in polar terms, it is the line whose distance from any point on the
conic makes a constant ratio with the distance between that point and the focus.
Eccentricity

The ratio
in an ellipse or hyperbola. Under the polar
definition of conics,
e
is the constant ratio of the distance from a point
to the focus and the distance from that point to the directrix.
Ellipse

The set of all points such that the sum of the distances from the point to each
of two fixed points is constant.
Focus

For a parabola, the point whose distance from any point on the parabola is
the same as the distance between that point and the directrix. For an
ellipse, one of two pointsthe sum of whose distances to a point on the
ellipse is constant. For a hyperbola, one of two pointsthe difference of
whose distances to a point on the hyperbola is constant. Under the polar
definition of a conic, it is the point whose distance from a point on the
conic makes a constant ratio with the distance between that point and the
directrix.
Hyperbola

The set of all points such that the difference of the distances between each of
two fixed points and any point on the hyperbola is constant.
Major Axis

The line segment containing the foci of an ellipse whose endpoints are
the vertices whose length is
2a
.
Minor Axis

The line segment containing the center of an ellipse perpendicular to
the major axis whose length is
2b
.
Parabola

The set of all points such that the distance between a point on the parabola and
a fixed line is the same as the distance between a point on the parabola and a
fixed point.
Radius

A segment between the center of a circle and a point on the circle, or
sometimes, the length of that segment.
Transverse Axis

The line segment that contains the center and whose endpoints are the two
vertices of a hyperbola.
Vertex

(Plural = "vertices") For a parabola, the point halfway between the focus and the
directrix. For an ellipse, one of two points where the line that
contains the foci intersects the ellipse. For a hyperbola, one of two
points at which the line containing the foci intersects the hyperbola.
Polar Form of a Conic

r = , orr =
, where
e
is the eccentricity of the conic, the
pole is the focus,
and
p
is the distance between the focus and the directrix.

Standard Form of a Circle

The standard equation for a circle is
(x  h)^{2} + (y  k)^{2} = r
^{2}
. The
center is at
(h, k)
. The radius is
r
.

Standard Form of an Ellipse

The standard equation of an ellipse with a horizontal major axis is the
following:
+ = 1
. The center is at
(h, k)
. The length of the major axis is
2a
, and the length of the minor
axis is
2b
. The distance between the center and either focus is
c
,
where
c
^{2} = a
^{2}  b
^{2}
.
a > b > 0
. The standard equation of an ellipse with
a vertical major axis is the following:
+ = 1
. The center is at
(h, k)
. The length of the major axis is
2a
, and the length of the minor axis is
2b
. The distance between the center
and either focus is
c
, where
c
^{2} = a
^{2}  b
^{2}
.
a > b > 0
.

Standard Form of a Hyperbola

The standard equation for a hyperbola with a horizontal transverse axis
is
 = 1
. The center is at
(h, k)
. The distance between the vertices is
2a
. The distance between
the foci is
2c
.
c
^{2} = a
^{2} + b
^{2}
. The standard equation for a hyperbola
with a vertical transverse axis is
 = 1
. The center is at
(h, k)
. The distance between the vertices
is
2a
. The distance between the foci is
2c
.
c
^{2} = a
^{2} + b
^{2}
.

Standard Form of a Parabola

If a parabola has a vertical axis, the standard form of the equation of
the parabola is this:
(x  h)^{2} = 4p(y  k)
, where
p≠ 0
. The
vertex of this parabola is at
(h, k)
. The focus is at
(h, k + p)
.
The directrix is the line
y = k  p
. The axis is the line
x = h
. If a
parabola has a horizontal axis, the standard form of the equation of the
parabola is this:
(y  k)^{2} = 4p(x  h)
, where
p≠ 0
. The vertex of
this parabola is at
(h, k)
. The focus is at
(h + p, k)
. The directrix is
the line
x = h  p
. The axis is the line
y = k
.
