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Ellipse ppt Presentation Transcript

  • 1. Ellipse © Jill Britton, September 25, 2003•Statuary Hall in the U.S. Capital building is elliptic. It was in this room that John QuincyAdams, while a member of the House of Representatives, discovered this acousticalphenomenon. He situated his desk at a focal point of the elliptical ceiling, easilyeavesdropping on the private conversations of other House members located near theother focal point.
  • 2. •An ellipse is the set of all points in a plane such that the sum of the distances from two fixed points is constant. Major Axis = 2a Minor Axis = 2b Major Axis = 2a(x-h)2 + (y-k)2 = 1 (y-k)2 + (x-h)2 = 1 a2 b2 a2 b2 Center = (h, k) *The larger denominator indicates the Major Axis*
  • 3. Writing an equation based on a graph•Write an equation for theellipse pictured.
  • 4. Writing equations given information1) Major axis 8 units long and parallel to x-axis, minor axis 2 unitslong and parallel to y-axis, center at (-2, 5).2) Endpoints of the major axis (-7, 2) and (5, 2), endpoints of minoraxis (-1, 0) and (-1, 4)
  • 5. Graphing Ellipses•Find the coordinates of the center and the lengths of the majorand minor axes for the ellipse within the given equation. Thengraph the ellipse.1) 2)
  • 6. HW: Worksheet