What are the equations for a hyperbolas with a horizontal and vertical transverse axis

The video tutorial covers the characteristics of hyperbolas, comparing them to ellipses. It explains the formula for hyperbolas, emphasizing the importance of subtraction in the definition and calculations. The tutorial also discusses how to determine whether a hyperbola has a vertical or horizontal transverse axis, and provides clarifications on axis size and additional notes.

What is the role of the center in a hyperbola?

• It is the midpoint of the transverse axis.

• It is the midpoint of the conjugate axis.

• It is the midpoint of the major axis.

• It is the midpoint of the minor axis.

In the formula of a hyperbola, what operation is used between the distances?

• Multiplication

• Addition

• Subtraction

• Division

Why is it important to maintain the order of subtraction in a hyperbola's formula?

• To match the ellipse formula

• To make the equation symmetrical

• To simplify the equation

• To ensure the correct constant is used

How can you determine if a hyperbola has a horizontal transverse axis?

• If 'b' is under the x-term

• If 'a' is under the y-term

• If 'b' is under the y-term

• If 'a' is under the x-term

What distinguishes the transverse axis of a hyperbola from the major axis of an ellipse?

• The transverse axis is not necessarily the longest axis.

• The transverse axis is always horizontal.

• The transverse axis is always vertical.

• The transverse axis is always the longest axis.

In a hyperbola, what is always true about the relationship between a^2 and b^2?

• a^2 is always subtracted from b^2

• a^2 is always greater than b^2

• b^2 is always greater than a^2

• b^2 is always subtracted from a^2

What should be the focus when dealing with the sizes of 'a' and 'b' in hyperbolas?

• Focusing on the subtraction of squares

• Ensuring b^2 is always larger

• Ensuring a^2 is always larger

• Comparing their absolute sizes