Dias nummer 1 - TeacherTube...definition of Conic Section nondegenerate curves, which are...
Transcript of Dias nummer 1 - TeacherTube...definition of Conic Section nondegenerate curves, which are...
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definition of Conic Section
nondegenerate curves,
which are intersections of
plane and cone
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central conics
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definition of ellipse
A conic section, which is essentially
a stretched circle
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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
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a
b a ≠ b
a = b
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major axis
minor axis
semi-major axis
semi-m
inor axis
semi-major axis = major axis
2
semi-minor axis = minor axis
2
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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
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definition of ellipticity
difference between the lengths of
the major axis and the minor axis
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Ellipticity is expressed as
a – b a
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b
a c
focus c2 = a2 – b2
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F1
F2
C X
0, y
0
2b
minor axis
2c
2a major axis r
1 + r
2 = 2a
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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
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construct cylinder from ellipse
planar curve r ≠ d
r d ellipse
cylinder 3-dimensional 2 circular/elliptical sides one curved side
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construct cone from ellipse
planar curve r ≠ d
r d ellipse
cone 3-dimensional 1 circular/elliptical base
one curved side one apex point
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circle
ellipse
parabola
hyperbola
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a = c
a ≠ c
spheroid
ellipsoid
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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