Ellipses - PowerPoint PPT Presentation

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Ellipses

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Complete the square for both the x-terms and y-terms and move the constant to ... the center to get the end points (horizontally if under x, vertically if under y) ... – PowerPoint PPT presentation

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Title: 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.
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