F1 и F2 - focal points of ellipse
Axes of ellipse.
А1А2 = 2a - major axis (larger direct that crosses focal points F1 and F2)
B1B2 = 2b - minor axis (smaller direct that perpendicular to major axis and intersect it at the center of the ellipse О)
a - semi-major axis
b - semi-minor axis
O - center of the ellipse
Vertices of ellipse A1, A2, B1, B2
Diameter of ellipse - is any straight line segment that passes through the center of the ellipse and whose endpoints lie on the ellipse.
Linear eccentricity c - is the distance from the focal point to the center of the ellipse.
Eccentricity of ellipse e
is the ratio of the linear eccentricity c
to the length of the semi-major axis a
. The eccentricity of an ellipse always be 0 < e
< 1, the eccentricity of the circle is e
= 0, the eccentricity of the parabola is e
= 1, the eccentricity of the hyperbola is e
Focal radius of ellipse r1, r2 is a distances from point on ellipse to focal point.
Radius of an ellipse
R - is a distance from ellipse the center to point (Мn
) at ellipse.
|R = ||ab|| = ||b|
|√a2sin2φ + b2cos2φ||√1 - e2cos2φ|
- eccentricity, а φ
- the angles within the radius (R) and major axis A1
Focal parameter of ellipse p
- is the focal radius that perpendicular to ma axis:
Flattening (ellipticity) of ellipse
is a measure of the compression of a circle along a semi-minor axis. Since the semi-minor axis of the ellipse is always smaller then semi-major axis, then k
< 1, and for circle k
f = 1 - √1 - e2,
Directrix of ellipse (1 - k ) is a line parallel to the minor axis and no touch to the ellipse. The distance from any point M on the ellipse to the focus F is a constant fraction of that points perpendicular distance to the directrix, resulting in the equality p/e.