Algebra II - Ellipse Day #2 NotesName______

Writing Equations of Ellipses

Four things are needed in order to write an equation of an ellipse:

1. the center

2. the value of

3. the value of

4. whether the ellipse is vertical or horizontal

Ex. #1: Make a quick sketch of the ellipse described. Then use the sketch to help write the equation of an ellipse with following properties:

Vertices at (-10, -2) and (0, -2)center ______

Co-vertices at (-5, 0) and (-5, -4)

______

______

vertical or horizontal

Equation: ______

If only or is known, sometimes must be used to calculate the other crucial missing variable. The formula would be needed to achieve this.

Ex. #2: Make a quick sketch of the ellipse described. Then use the sketch to help write the equation of an ellipse with the following properties:

Vertices at (4, 8) and (4, -4)

Foci at (4, 4) and (4, 0)center ______

______

______

______

vertical or horizontal

Equation: ______

Ex. #3: Make a quick sketch of the ellipse described. Then use the sketch to help write the equation of an ellipse with the following properties:

Coordinate of the center: (3, -5)

Length of major axis: 20

Length of minor axis: 8center ______

Major axis parallel to x-axis

______

______

vertical or horizontal

Equation: ______

Ex. #4: Make a quick sketch of the ellipse described. Then use the sketch to help write the equation of an ellipse with the following properties:

Ellipse is a vertical

Coordinate of the center: (2, 4)

Length of major axis: 12center ______

______

______

vertical or horizontal

Equation: ______

Ex. #5: Make a quick sketch of the ellipse described. Then use the sketch to help write the equation of an ellipse with the following properties:

Foci are at (-12, 3) and (-2, 3)

Length of minor axis: 10center ______

______

______

______

vertical or horizontal

Equation: ______