What is the definition of a hyperbola

The video tutorial reviews the properties of parabolas, ellipses, and hyperbolas, focusing on their definitions and characteristics. It begins with a discussion on parabolas, highlighting the role of the focus and directrix. The tutorial then transitions to ellipses, explaining the sum of distances from any point on the ellipse to the foci. Finally, the video introduces hyperbolas, detailing their unique properties, such as the transverse axis and the difference of distances from any point on the hyperbola to the foci.

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 and directrix is equal.

• The parabola always opens upwards.

• The parabola has no directrix.

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

When two parabolas are combined to form an ellipse, what remains constant?

• The angle between the parabolas.

• The distance from any point to the directrix.

• The sum of distances from any point to the two foci.

• The difference in distances from any point to the two foci.

What is the transverse axis in a hyperbola?

• The line that bisects the angle between the asymptotes.

• The line that is perpendicular to the directrix.

• The line that connects the vertices and the center.

• The line that connects the two foci.

In a hyperbola, how are the distances from any point to the two foci related?

• Their sum is constant.

• They are always perpendicular.

• Their difference is constant.

• They are always equal.

How do the vertices of a hyperbola compare to its foci?

• The vertices are further from the center than the foci.

• The vertices are closer to the center than the foci.

• The vertices and foci are equidistant from the center.

• The vertices are on the directrix.

What is a key difference between an ellipse and a hyperbola?

• In an ellipse, the sum of distances to the foci is constant, while in a hyperbola, the difference is constant.

• A hyperbola has a directrix, while an ellipse does not.

• An ellipse has a transverse axis, while a hyperbola does not.

• An ellipse always has a vertical major axis.

What happens to the distances from any point on a hyperbola to the two foci?

• They are always perpendicular.

• Their difference is constant.

• Their sum is constant.

• They are always equal.