Conic Sections
Ellipse
The Sequal
1
Eccentricity
• A measure of the "roundness" of an ellipse
not so round
very round
2
Eccentricity
• Given measurements of an ellipse


c = distance from center to focus
a = ½ the
length of the
major axis
• Eccentricity
c
e
a
3
Eccentricity
• What limitations can we place on c in
relationship to a?

c< a
• What limitations
does this put on
c
e
a
?
• When e is close to 0, graph almost a circle
• When e close to 1, graph long and thin
4
Finding the Eccentricity
• Given an ellipse with



Center at (2,-2)
Vertex at (7,-2)
Focus at (4,-2)
• What is the eccentricity?
• Remember that c  a  b
2
2
2
5
Using the Eccentricity
• Consider an ellipse with e = ¾

Foci at (9,0) and (-9,0)
• What is the equation
of the ellipse in standard
form?
6
Acoustic Property of Ellipse
• Sound waves emanating from one focus will
be reflected


Off the wall of the ellipse
Through the opposite focus
View Animation
7
Whispering Gallery
• At Chicago Museum
of Science and
Industry
The Whispering Gallery is
constructed in the form of an
ellipsoid, with a parabolic dish at
each focus. When a visitor stands
at one dish and whispers, the line
of sound emanating from this focus
reflects directly to the dish/focus at
the other end of the room, and to
the other person!
8
Elliptical Orbits
• Planets travel in elliptical orbits around the
sun

Or satellites around the earth
9
Elliptical Orbits
• Perihelion

Distance from focus to closest approach
• Aphelion

Distance from focus to farthest reach
• Mean Distance

Mean
Dist
Half the major
axis
10
Elliptical Orbits
• The mean distance of Mars from the Sun is
142 million miles.



Perihelion = 128.5 million miles
Aphelion = ??
Equation for Mars orbit?
Mars
11
Assignment
• Ellipses B
• 45 – 63 odd
12