Conic Sections Ellipse The Sequal

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

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

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

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

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?

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

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!

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

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

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

Assignment Ellipses B 45 – 63 odd