1. Advanced Geometry Conic Sections Lesson 4
Ellipses & Hyperbolas

2. Ellipses
Minor Axis
Definition – the set of all points in a plane that the sum of the distances from two given points, called the foci, is constant V
Major Axis F C F V V V

3. Equation
(a² > b²)
Center
Foci
equation
vertices
Major Axis
Minor Axis

4. Example:
For the equation of each ellipse or hyperbola, find all information
listed. Then graph.
Center:
Foci:
Length of the
major axis:
minor axis:

5. Hyperbola
Definition – the set of all points in a plane that the absolute value of the distance from two given points in the plane, called the foci, is constant
Asymptote F V
Conjugate Axis C V
Asymptote F
Transverse Axis

6. Equation of a Hyperbola Slopes of the Asymptotes
Center
Foci
Vertices
Slopes of the Asymptotes
Direction of Opening

7. Example:
For the equation of each ellipse or hyperbola, find all information
listed. Then graph.
Center:
Vertices:
Foci:
Slopes of the
asymptotes:

8. Example:
Using the graph below, write the equation for the ellipse or hyperbola.

9. Example:
Using the graph below, write the equation for the ellipse or hyperbola.

10. Write the equation of the ellipse or hyperbola that meets
Example:
Write the equation of the ellipse or hyperbola that meets
each set of conditions.
The foci of an ellipse are (-5, 3) and (3, 3) and the
minor axis is 6 units long.

11. Write the equation of the ellipse or hyperbola that meets
Example:
Write the equation of the ellipse or hyperbola that meets
each set of conditions.
The vertices of a hyperbola are (0,-3) and (0, -8) and the
length of the conjugate axis is units long.

12. Example:
Write each equation in standard form. Determine if it is an ellipse or a hyperbola.