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: ______