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Conic Sections

Conic Sections. The Ellipse Part A. Ellipse. Another conic section formed by a plane intersecting a cone Ellipse formed when. Definition of Ellipse. Set of all points in the plane … Sum of distances from two fixed points (foci) is a positive constant. Definition of Ellipse.

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Conic Sections

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  1. Conic Sections The EllipsePart A

  2. Ellipse • Another conicsection formedby a plane intersecting acone • Ellipse formed when

  3. Definition of Ellipse • Set of all points in the plane … • Sum of distances from two fixed points(foci) is a positive constant

  4. Definition of Ellipse • Definition demonstrated by using two tacks and a length of string to draw an ellipse

  5. Graph of an Ellipse Note various parts of an ellipse

  6. Deriving the Formula • Note • Why? • Write withdist. formula • Simplify

  7. Major Axis on y-Axis • Standard form of equation becomes • In both cases • Length of major axis = 2a • Length of minor axis = 2b Link to Animated Web Page

  8. Using the Equation • Given an ellipse with equation • Determine foci • Determine values for a,b, and c • Sketch the graph

  9. Find the Equation • Given that an ellipse … • Has its center at (0,0) • Has a minor axis of length 6 • Has foci at (0,4) and (0,-4) • What is the equation?

  10. Ellipses with Center at (h,k) • When major axis parallelto x-axis equation can be shown to be

  11. Ellipses with Center at (h,k) • When major axis parallelto y-axis equation can be shown to be

  12. Find Vertices, Foci • Given the following equations, find the vertices and foci of these ellipses centered at (h, k)

  13. Find the Equation • Consider an ellipse with • Center at (0,3) • Minor axis of length 4 • Focci at (0,0) and (0,6) • What is the equation?

  14. Assignment • Ellipses A • 1 – 43 Odd

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