how to identify a b and c for an hyperbola then graph

The video tutorial explains how to work with hyperbolas, starting with identifying key components like A, B, and C. It covers calculating distances to vertices, co-vertices, and foci, and explains the equation for C. The tutorial then demonstrates how to graph the hyperbola, identify the center, and find the transverse axis. It also shows how to find and draw asymptotes using vertices and co-vertices, and concludes with deriving the equation of asymptotes and summarizing the key points.

What is the relationship between a, b, and c in a hyperbola?

• c^2 = b^2 - a^2

• c^2 = a^2 + b^2

• c^2 = a^2 - b^2

• c^2 = a^2 * b^2

In a hyperbola, what does the term 'a' represent?

• Distance from center to co-vertices

• Distance from center to foci

• Distance from center to vertices

• Distance from center to asymptotes

What is the orientation of the transverse axis in this hyperbola?

• Vertical

• Diagonal

• Horizontal

• Circular

How do you determine the position of the foci in a hyperbola?

• By using the equation c^2 = a^2 * b^2

• By using the equation c^2 = a^2 - b^2

• By using the equation c^2 = a^2 + b^2

• By using the equation c^2 = b^2 - a^2

What is the purpose of drawing a box with co-vertices and vertices in a hyperbola?

• To determine the foci

• To calculate the eccentricity

• To find the center

• To graph the asymptotes

What is the equation of the asymptotes for a horizontal hyperbola?

• y = ± (a/b) * x + k

• y = ± (b/a) * x + h

• y = ± (a/b) * x

• y = ± (b/a) * x

What are the coordinates of the center of the hyperbola discussed?

• (±sqrt(41), 0)

• (±4, 0)

• (0, ±5)

• (0, 0)