#### Objectives

- Students will be able to define an ellipse as the set of points whose distances to two fixed points (foci) have a constant sum.
- Students will be able to define a hyperbola as the set of points whose distances to two fixed points (foci) have a constant difference.
- Students will be able to describe the relationship between the location of the foci and the shapes of the corresponding ellipses and hyperbolas.
- Students will be able to determine the effect of the eccentricity of ellipses and hyperbolas on the shape of their curves.

#### Vocabulary

- conjugate axis
- eccentricity
- ellipse
- focus/foci
- hyperbola
- major axis
- minor axis
- semi-major axis
- semi-minor axis
- transverse axis
- vertex of a conic

#### About the Lesson

This lesson involves observing and describing the relationships between the foci of ellipses and hyperbolas and the shape of the corresponding curves.

As a result, students will:

- Define an ellipse as the set of points whose distances to two fixed points (foci) have a constant sum.
- Define a hyperbola as the set of points whose distances to two fixed points (foci) have a constant difference.
- Manipulate sliders to observe the relationship between the foci and sum/difference of the distances from the foci to a point on the curve.
- Observe the effect of the relationship between the foci and the shapes of ellipses or hyperbolas.