Ellipse, Parabola, Hyperbola
Ellipse with center
and major axis parallel to
axis
Length of major axis
Length of minor axis
Distance from center to focus
or
is
Eccentricity =
Equation in rectangular coordinates:
Equation in polar coordinates if is at
:
Equation in polar coordinates if is on
axis and
is at
:
If is any point on the ellipse,
If the major axis is parallel to the axis, interchange
and
in the above or replace
by
[or
]
Parabola with axis parallel to
axis
If vertex is at and the distance from
to focus
is
, the equation of the parabola is if parabola opens to right
If parabola opens to left
If focus is at the origin the equation in polar coordinates is
In case the axis is parallel to the axis, interchange
and
or replace
by
[or
].
Hyperbola with center
and major axis parallel to
axis
Length of major axis
Length of minor axis
Distance from center to focus
or
is
Eccentricity =
Equation in rectangular coordinates:
Slopes of asymptotes and
Equation in polar coordinates if is at
:
Equation in polar coordinates if is on
axis and
is at
:
If is any point on the hyperbola,
[depending on branch]
If the major axis is parallel to the axis, interchange
and
in the above or replace
by
[or
].

