What is the definition of an ellipse

The video tutorial reviews the definition of a parabola, focusing on the concepts of focus and directrix, and explains that any point on a parabola is equidistant from the focus and directrix. It then introduces ellipses, describing them as distorted circles or two parabolas focusing on each other. The key property of an ellipse is that the sum of the distances from any point on the ellipse to the two foci is constant. This property is explained with examples, emphasizing the difference from parabolas.

What is the defining characteristic of a parabola in relation to its focus and directrix?

• The distance from any point on the parabola to the focus is equal to the distance to the directrix.

• The distance from any point on the parabola to the focus is greater than to the directrix.

• The distance from any point on the parabola to the focus is less than to the directrix.

• The distance from any point on the parabola to the focus is twice the distance to the directrix.

How can an ellipse be visually described?

• As a square with rounded corners.

• As a distorted circle or two parabolas facing each other.

• As a perfect circle.

• As a triangle with curved sides.

What is the role of the foci in the definition of an ellipse?

• The sum of the distances from any point on the ellipse to the two foci is constant.

• The foci are irrelevant to the shape of the ellipse.

• The foci determine the width of the ellipse.

• The foci are always located at the center of the ellipse.

What remains constant for any point on an ellipse?

• The distance from the point to the center of the ellipse.

• The angle between the point and the foci.

• The sum of the distances from the point to both foci.

• The distance from the point to one focus.

How does the definition of an ellipse differ from that of a parabola?

• An ellipse involves the sum of distances to two foci, while a parabola involves equal distances to a focus and directrix.

• A parabola has two foci, while an ellipse has one.

• An ellipse has a directrix, while a parabola does not.

• A parabola is a type of ellipse.