definition of Conic Section

nondegenerate curves,

which are intersections of

plane and cone

central conics

definition of ellipse

A conic section, which is essentially

a stretched circle

structural definition of ellipse

A curved line, forming a closed loop,

where the sum of the distances

from the two foci to every point on the line

is constant

a

b a ≠ b

a = b

major axis

minor axis

semi-major axis

semi-m

inor axis

semi-major axis = major axis

2

semi-minor axis = minor axis

2

properties of ellipse

minor axis

major axis longest diameter of ellipse

shortest diameter of ellipse

center intersection of major and minor axes

focus 2 points defining elliptical shape, equally spaced from the center

perimeter distance around the ellipse

chord line segment linking 2 points on the elliptical parameter

definition of ellipticity

difference between the lengths of

the major axis and the minor axis

Ellipticity is expressed as

a – b a

b

a c

focus c2 = a2 – b2

F1

F2

C X

0, y

0

2b

minor axis

2c

2a major axis r

1 + r

2 = 2a

perfectly round ball

has no open end

same distance from the center in all directions

construct sphere from circle

radi

us curved line

= circumference

= radius

3-dimensional

sphere

construct cylinder from ellipse

planar curve r ≠ d

r d ellipse

cylinder 3-dimensional 2 circular/elliptical sides one curved side

construct cone from ellipse

planar curve r ≠ d

r d ellipse

cone 3-dimensional 1 circular/elliptical base

one curved side one apex point

circle

ellipse

parabola

hyperbola

a = c

a ≠ c

spheroid

ellipsoid

useful links

https://www.mathsisfun.com/geometry/eccentricity.html

https://www.mathopenref.com/ellipse.html

http://www.differencebetween.info/difference-between-parabola-and-hyperbola

http://mathworld.wolfram.com/Ellipse.html

http://www.math.com/tables/algebra/conics.htm

https://www.math10.com/en/geometry/

https://shelovesmath.com/precal/conics/

http://www.mathcaptain.com/geometry/eccentricity.html

http://www.mathwarehouse.com/ellipse/eccentricity-of-ellipse.php

https://study.com/academy/lesson/eccentricity-of-conic-sections.html

http://www.braeunig.us/space/orbmech.htm

http://mathworld.wolfram.com/ConicSection.html