What is the definition of an ellipse for conic sections

The video tutorial explains the concept of an ellipse, comparing it to a circle. It defines an ellipse as a set of points where the sum of distances to two fixed points, called foci, is constant. The tutorial elaborates on the properties of ellipses, including the role of foci and how these properties differ from those of a circle. The video concludes by summarizing the key points and highlighting the similarities and differences between ellipses and circles.

How is an ellipse similar to a circle?

• Both have points equidistant from the center.

• Both are defined by a set of points.

• Both have a constant radius.

• Both are perfect circles.

What is unique about the distances from any point on an ellipse to its foci?

• They vary randomly.

• They are always zero.

• Their sum is constant.

• They are always equal.

What are the two fixed points in an ellipse called?

• Centers

• Vertices

• Axes

• Foci

In what way does the definition of an ellipse differ from that of a circle?

• An ellipse is a perfect circle.

• An ellipse has a constant sum of distances to two foci.

• An ellipse has two centers.

• An ellipse has a constant radius.

How does the concept of an ellipse relate to that of a circle?

• An ellipse is a distorted circle.

• An ellipse shares some properties with a circle.

• An ellipse is a type of circle.

• An ellipse is unrelated to a circle.