 You probably know the ellipse by its more well-known name: the oval.  An ellipse looks like a circle that has been stretched out.

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Presentation transcript:

 You probably know the ellipse by its more well-known name: the oval.  An ellipse looks like a circle that has been stretched out.

An ellipse is a type of conic section: a two dimensional shape that is generated by taking a cross-section of a cone. Specifically, if you take a cross section of a cone at a slight angle, you get an ellipse. This puts ellipses in the same category as circles, parabolas, and hyperbolas.

 An ellipse is the set of all points where the sum of the distances from two points inside the ellipse to every point on the ellipse is constant.  These two points are known as the foci.  In the diagram to the right, this means x+y is constant.

An ellipse has two axes: the major axis, which is the longest line through the ellipse, and the minor axis, which is the shortest line. In this diagram, the major axis goes from –a to a and the minor axis goes from –b to b. An ellipse has a center, just like a circle. The center lies on the intersection of the two axes. An ellipse has two vertices: the two points on either side of the major axis. This is where the ellipse turns most sharply.

Conic Section: a curve obtained by intersecting a cone with a plane. Foci: The two points that define an ellipse. The total distance from each point on the ellipse to the two foci is constant. Major Axis: The line between the two points on an ellipse that are furthest apart. Minor Axis: The perpendicular bisector of the major axis and the shortest line through an ellipse. Vertex: The two points on either end of the major axis. Center: The intersection of the major axis and the minor axis.