Algebra II/Trigonometry Honors
Unit 8 Day 4: Graph and Write Equations of Ellipses
Objective: To graph and write the equations of ellipses
Key Terms:

Ellipse - ___________________________________________________________________

Foci - _____________________________________________________________________

Major Axis - ________________________________________________________________

Minor Axis - ________________________________________________________________

Vertices - __________________________________________________________________

Co-vertices - _______________________________________________________________
Standard Equation of an Ellipse with Center at the Origin
Equation
Major Axis
Vertices
Co-Vertices
x2 y2

1
a2 b2
Horizontal
 a,0
0,b
x2 y2

1
b2 a2
Vertical
0,a
 b,0
* a b0
The length of the major axis is 2a . The length of the minor axis is 2b .
The foci of the ellipse lie on the major axis at a distance of c units from the center. c 2  a 2  b 2
Example 1: Graph an equation of an ellipse
Graph the equation 4 x 2  25 y 2  100 . Identify the vertices, co-vertices, and foci of the ellipse.
Example 2: Write an equation given a vertex and a co-vertex
Write an equation of the ellipse that has a vertex at (0, 4), a co-vertex at (-3, 0), and center at (0, 0).
Example 3: Solve a multi-step problem
When lightning strikes, an elliptical region where the strike most likely hit can often be identified.
Suppose it is determined that there is a 50% chance that a lightning strike hit within the elliptical region
shown in the diagram.
 Write an equation of the ellipse.
 The area A of an ellipse is A  ab . Find the area of the elliptical region.
Example 4: Write an equation given a vertex and a focus
Write an equation of the ellipse that has a vertex at (-8, 0), a focus at (4, 0), and center at (0, 0).
HW: Page 513 #3-42 (M3), 50