Ellipse Review (11/15/24)

Front

What is the standard form of the equation of an ellipse with a horizontal major axis?

Back

Front

What is the standard form of the equation of an ellipse with a vertical major axis?

Back

Front

What do the variables h and k represent in the ellipse equation?

Back

The variables h and k represent the coordinates of the center of the ellipse (h, k).

Front

How do you determine the lengths of the major and minor axes of an ellipse?

Back

The lengths are determined by the values of a and b in the standard form: Major axis length = 2a, Minor axis length = 2b.

Front

What is the relationship between a, b, and the foci of an ellipse?

Back

Front

What is the definition of an ellipse?

Back

An ellipse is the set of all points in a plane such that the sum of the distances from two fixed points (foci) is constant.

Front

How can you identify the orientation of an ellipse from its equation?

Back

If a^2 is under the x-term, the ellipse has a horizontal major axis; if a^2 is under the y-term, it has a vertical major axis.

Front

What are the coordinates of the vertices of an ellipse with a horizontal major axis?

Back

The vertices are located at (h ± a, k).

Front

What are the coordinates of the vertices of an ellipse with a vertical major axis?

Back

The vertices are located at (h, k ± a).

Front

How do you find the co-vertices of an ellipse?

Back

The co-vertices are located at (h ± b, k) for horizontal major axis and (h, k ± b) for vertical major axis.