Lecture #7 analytic geometry

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Lecture #7 analytic geometry

  1. 1. Lecture #7 Ellipse Parts of Ellipse and its graph • Equation of Ellipse - Standard Equation - General Equation • Formulas
  2. 2. ELLIPSE  An ellipse is defined by two points, each called a focus. If you take any point on the ellipse, the sum of the distances to the focus points is constant.
  3. 3. PARTS OF AN ELLIPSE  Vertices – the points at which an ellipse makes its sharpest turns and lies on the major axis, also end of major axis  Co-vertices – ends of minor axis  Focus/foci – point/s that define the ellipse and lies on the major axis  Major axis – the longest diameter of the ellipse  Minor axis – the shortest diameter of the ellipse
  4. 4. EQUATIONS OF ELLIPSE 
  5. 5. EQUATIONS OF ELLIPSE 
  6. 6. EQUATIONS OF ELLIPSE 
  7. 7. EQUATIONS OF ELLIPSE 
  8. 8.
  9. 9. FORMULAS (if center is at the origin and major axis at x- axis) Vertices Co-vertices (a, 0) (-a, 0) (0, b) (0, -b) Foci Length of LR (c, 0) (-c, 0) Length of major and minor axis 2a (major) 2b (minor) Ends of Latera recta
  10. 10. FORMULAS (if center is at the origin and major axis at y- axis) Vertices Co-vertices (0, a) (0, -a) (b, 0) (-b, 0) Foci Length of LR (0, c) (0, -c) Length of major and minor axis 2a (major) 2b (minor) Ends of Latera recta
  11. 11. FORMULAS (if center is at (h, k) and major axis at x-axis) Vertices Co-vertices (h + a, k) (h - a, k) (h, k + b) (h, k-b) Foci Length of LR (h + c, k) (h - c, k) Length of major and minor axis 2a (major) 2b (minor) Ends of Latera recta
  12. 12. FORMULAS (if center is at (h, k) and major axis at y-axis) Vertices Co-vertices (h, k + a) (h, k - a) (h + b, k) (h - b, k) Foci Length of LR (h, k + c) (h, k - c) Length of major and minor axis 2a (major) 2b (minor) Ends of Latera recta
  13. 13. Sample Problem 

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