An ellipse is commonly known as an oval. Ellipses are just as common as parabolas in the real world with their own uses. Rooms that have elliptical shaped ceilings are called whisper rooms because if you stand at one focus point and whisper, someone standing at the other focus point will be able to hear you.
The general equation for an ellipse is:
Once you have the focal radius, measure from the center along the major axis to locate the foci. The general shape of an ellipse is measured using eccentricity. Eccentricity is a measure of how oval or how circular the shape is. Ellipses can have an eccentricity between 0 and 1 where a number close to 0 is extremely circular and a number close to 1 is less circular. Eccentricity is calculated by:
Find the vertices (endpoints of the major axis), foci and eccentricity of the following ellipse.
The focal radius is 3. This means that the foci are at (3, 0) and (-3, 0).
Sketch the following ellipse.
Put the following conic into graphing form.
Concept Problem Revisited
Ellipses are measured using their eccentricity. Here are three ellipses with estimated eccentricity for you to compare.
The major axis is the longest distance from end to end of an ellipse. This distance is twice that of the semi-major axis.
An ellipse is the collection of points whose sum of distances from two foci is constant.
The foci in an ellipse are the two points that the ellipse curves around.
1. Find the vertices (endpoints of the major axis), foci and eccentricity of the following ellipse.
2. Sketch the following ellipse.
3. Put the following conic into graphing form.