1 / 13

Conic Sections

Conic Sections. Ellipse The Sequal. Deriving the Formula. Consider P at (0, b) Isosceles triangle Legs = a And. a. a. Eccentricity. A measure of the "roundness" of an ellipse. not so round. very round. Eccentricity. Given measurements of an ellipse c = distance from center to focus

lavi
Download Presentation

Conic Sections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Conic Sections EllipseThe Sequal

  2. Deriving the Formula • Consider P at (0, b) • Isoscelestriangle • Legs = a • And a a

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

  4. Eccentricity • Given measurements of an ellipse • c = distance from center to focus • a = ½ thelength of the major axis • Eccentricity

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

  6. 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

  7. Using the Eccentricity • Consider an ellipse with e = ¾ • Foci at (9,0) and (-9,0) • What is the equationof the ellipse in standardform?

  8. 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

  9. Whispering Gallery • At Chicago Museumof Science andIndustry 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!

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

  11. Elliptical Orbits • Perihelion • Distance from focus to closest approach • Aphelion • Distance from focus to farthest reach • Mean Distance • Half the majoraxis MeanDist

  12. 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

  13. Assignment • Ellipses B • 45 – 63 odd

More Related