1. Lecture #7
Ellipse
Parts of Ellipse and its graph
• Equation of Ellipse
- Standard Equation
- General Equation
• Formulas

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. 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

5. EQUATIONS OF ELLIPSE
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6. EQUATIONS OF ELLIPSE
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7. EQUATIONS OF ELLIPSE
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8. EQUATIONS OF ELLIPSE
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9. 

10. 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

11. 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

12. 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

13. 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

14. Sample Problem
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