Ellipses

1
Ellipses

• Topic 7.4

2
Definitions

• Ellipse set of all points where the sum of the
  distances from the foci is constant
• Major Axis axis on which the foci lie the
  longer axis of symmetry
• Minor Axis the shorter axis of symmetry

3
Two Standard Equations

• Horizontal Ellipse
• Foci
• Vertical Ellipse
• Foci

4
Writing in Standard Form

• Complete the square for both the x-terms and
  y-terms and move the constant to the other side
  of the equation
• Divide all terms by the constant

5
Example
Group terms
Complete the square
Simplify each group
Divide by constant
6
Graphing the ellipse

1. Put equation in standard form
2. Graph the center (h, k)
3. Graph the foci (look at the equation to determine
   your direction)
4. Graph a units and a units from the center to
   get the end points (horizontally if under x,
   vertically if under y)
5. Connect the end points!

7
Example
1) Graph Center
2) Graph Foci
3) Graph Endpoints
4) Graph Ellipse
8
You Try! Write the following equation in standard
form, then graph it.