1. Conic Sections
Ellipse The Sequal

2. Eccentricity A measure of the "roundness" of an ellipse not so round
very round

3. Eccentricity Given measurements of an ellipse Eccentricity
c = distance from center to focus
a = ½ the length of the major axis
Eccentricity

4. Eccentricity What limitations can we place on c in relationship to a?
What limitations does this put on
When e is close to 0, graph almost a circle
When e close to 1, graph long and thin

5. 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

6. 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?

7. 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

8. 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!

9. Elliptical Orbits Planets travel in elliptical orbits around the sun
Or satellites around the earth

10. Elliptical Orbits Perihelion Aphelion Mean Distance
Distance from focus to closest approach
Aphelion
Distance from focus to farthest reach
Mean Distance
Half the major axis
Mean Dist

11. Elliptical Orbits
The mean distance of Mars from the Sun is 142 million miles.
Perihelion = million miles
Aphelion = ??
Equation for Mars orbit?
Mars

12. Assignment
Ellipses B
45 – 63 odd