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 1. Complete the square for both the x- terms and y-terms and move the constant to the other side of the equation 2. 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.