The video tutorial explains how to write the equation of a hyperbola by first plotting the foci and identifying the transverse axis. It then guides through finding the center and vertices, calculating the necessary values, and finally writing the hyperbola equation. The tutorial emphasizes understanding the relationship between a^2, b^2, and c^2, and how to apply these to form the correct equation for a vertical hyperbola.

What is the first step in analyzing a hyperbola?

• Calculate the distance between the foci

• Determine the length of the transverse axis

• Plot the foci on a graph

• Find the center of the hyperbola

How is the center of a hyperbola determined?

• By measuring the distance from the origin

• By identifying the intersection of the asymptotes

• By calculating the average of the foci coordinates

• By finding the midpoint between the vertices

What does the transverse length of a hyperbola represent?

• The length of the conjugate axis

• The distance from the center to a vertex

• The distance between the foci

• The total distance between the vertices

Which equation represents the relationship between 'a^2', 'b^2', and 'c^2' in a hyperbola?

• c^2 = a^2 + b^2

• b^2 = a^2 - c^2

• a^2 = c^2 - b^2

• a^2 = b^2 + c^2

In the equation of a vertical hyperbola, which term is placed over 'a^2'?

• x^2

• b^2

• c^2

• y^2