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. Characteristics of Ellipses

4. Standard form Ellipse Equation: a > b > 0
The foci are on the major axis, c units from the
center, where c2 = a2 – b2
Equation Major Axis Vertices Co-Vertices
Horizontal ( a, 0) (0, b)
Vertical (0, a) ( b, 0)

5. Graphing
1. Write in standard form.
2. Use a and b to plot vertices and co-vertices.
3. Draw the ellipse connecting all 4 points.
Example:
Draw the ellipse given by
and identify the foci.

6. Your Turn!
 Graph and identify the foci.

7. Writing Equations
 Write an equation of the ellipse with the given
characteristics and center (0, 0).
 Vertex: (0, 7)
Co-Vertex: (-6, 0)
 Vertex: (-4, 0)
Focus: (2, 0)

8. Your Turn!
 Write an equation of the ellipse with center
(0,0) and:
 vertex at (3, 0)
 co-vertex at (0, -1)

9. Area of an Ellipse
 A = πab
Example:
A portion of the White House lawn is called The
Ellipse. It is 1060 feet long and 890 feet wide.
1. Write an equation of The Ellipse.
2. Find the area of The Ellipse.

10. Modeling with an Ellipse
 In it’s elliptical orbit, Mercury ranges from
46.04 million km to 69.86 million km from the
center of the sun, which is a focus of the
orbit. Write an equation of the orbit.