Given the graph and asymptotes write the equation for a hyperbola

The video tutorial explains how to write the equation for a hyperbola, focusing on determining whether the transverse axis is vertical or horizontal. It covers the equation for a hyperbola with a vertical transverse axis, identifying the center and vertices, and calculating the asymptotes and slope. The tutorial concludes with deriving the final equation of the hyperbola.

What is the first step in writing the equation for a hyperbola?

• Identify the transverse axis as vertical or horizontal

• Find the slope of the asymptotes

• Determine the center of the hyperbola

• Calculate the distance between the foci

How do you find the center of a hyperbola?

• By determining the distance from the center to the co-vertices

• By using the slope of the asymptotes

• By finding the midpoint between the vertices

• By calculating the midpoint between the foci

What is the equation for the asymptotes of a hyperbola with a vertical transverse axis?

• y = k ± a/b * (x - h)

• x = h ± a/b * (y - k)

• y = k ± b/a * (x - h)

• x = h ± b/a * (y - k)

How can you determine the value of 'b' for a hyperbola?

• By measuring the distance from the center to the co-vertices

• By finding the slope of the asymptotes

• By calculating the midpoint between the foci

• By using the distance from the center to the vertices

What is the final equation of the hyperbola discussed in the video?

• x^2/9 - y^2/5 = 1

• y^2/9 - x^2/5 = 1

• y^2/5 - x^2/9 = 1

• x^2/5 - y^2/9 = 1