6 3 ellipses

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6 3 ellipses

  1. 1. 6-3 Ellipses Objectives: 1. Graph ellipses. 2. Find equations of ellipses.
  2. 2. Definition of an Ellipse  Set of all points P such that the sum of the distances between P and the two foci (plural for “focus”) is constant. d1 + d2 = constant
  3. 3. Horizontal Major Axis:
  4. 4. Vertical Major Axis:
  5. 5. Finding Foci The foci are on the major axis, c units from the center, where c2 = a2 – b2 Remember a > b
  6. 6. Graphing Ellipses 1. Write in standard form. 2. Use a and b to plot vertices and co-vertices. 3. Sketch the ellipse.
  7. 7. Example:  Sketch the ellipse and identify the foci.
  8. 8. You Try! Graph and identify the foci.
  9. 9. Writing Equations Write an equation of the ellipse with the given characteristics and center (0, 0). Vertex: (0, 7) Minor axis 12 units long Vertex: (-4, 0) Focus: (2, 0)
  10. 10. You Try! Write an equation of the ellipse with center (0,0), vertex at (0, 4) and minor axis 4 units long. Find the coordinates of the foci.

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