Ellipse

• Ellipse: A ≠ B but both positive
• Standard Equation:

  (x-h)2/a2 + (y-k)2/b2 = 1
• If a2 comes first, it is horizontal.

  If b2 comes first, it is vertical.
• To determine the value of a and b, get the square root of both values and the bigger value represents a2.
• In determining the center, always remember that (h, k) = center and negative is positive and positive is negative.
• Axis of Symmetry:

  Major Axis (longer segment) = 2a

  Minor Axis (shorter segment) = 2b
• Vertex:

  Vertices (Major) - endpoints of major axis

  Co-vertices (Min) - CV1 and CV2
• Parts of an Ellipse:

  Foci - two fixed points in an ellipse, located on the major axis. It is labeled as F1 and F2.

  c2 = a2 - b2 (c units away from the center)
• Real-life Examples/Applications:

  Circles: Earthquakes, GS (determine the distance), architecture

  Ellipse: Lithotripsy, Whispering Chambers, Solar System
• What to include in graphing an ellipse:

  • Vertices
  • Co-vertices
  • Center
  • Foci (always on the major axis)

  What to include in solving for an ellipse: (ABCdius)

  • Value of a and b
  • Center
  • Radius (2a and 2b)