Writing the equation of a hyperbola given the foci and vertices

The video tutorial explains how to determine the orientation of a hyperbola's transverse axis, whether horizontal or vertical, by plotting points and analyzing the positions of vertices and foci. It guides through writing the hyperbola equation by identifying the center and calculating distances between vertices and foci. The tutorial concludes with finalizing the equation using the derived values of a, b, and c.

What are the two different orientations of the transverse axis for hyperbolas mentioned in the text?

How do you determine whether the transverse axis of a hyperbola is horizontal or vertical?

What is the significance of the vertices and foci in relation to the transverse axis?

How do you find the center of a hyperbola using the vertices and foci?

What is the importance of knowing the values of a^2, b^2, and c^2 when working with hyperbolas?

What is the relationship between a, b, and c in the context of hyperbolas?

How do you derive the standard form of the equation for a hyperbola?