Find the asymptotes, foci, vertices and center of a hyperbola

The video tutorial covers the identification and graphing of hyperbolas. It begins with recognizing the hyperbola and calculating the values of A^2, B^2, and C^2. The tutorial then demonstrates how to graph the hyperbola, identify the center, and determine the transverse and conjugate axes. It explains how to find the vertices and foci, sketch the asymptotes, and label all elements on the graph. Finally, it provides the equation for the hyperbola with a vertical transverse axis.

What is the relationship between A^2 and B^2 in a hyperbola?

• A^2 + B^2

• A^2 - B^2

• A^2 / B^2

• A^2 * B^2

How do you determine the center of a hyperbola?

• By finding the midpoint of the vertices

• By using the values of H and K

• By calculating the average of A and B

• By identifying the intersection of the axes

What lies on the transverse axis of a hyperbola?

• Center and asymptotes

• Co-vertices and asymptotes

• Vertices and co-vertices

• Vertices and foci

How do you sketch the asymptotes of a hyperbola?

• By connecting the vertices

• By drawing lines parallel to the axes

• By creating a box with the co-vertices

• By drawing diagonals through the center

What is the role of asymptotes in a hyperbola?

• They intersect at the center

• They guide the shape of the hyperbola

• They determine the length of the transverse axis

• They define the width of the hyperbola

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

• By using the distance of sqrt(C^2) from the center

• By finding the midpoint of the vertices

• By using the values of B and C

• By adding and subtracting A from the center

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

• y = ± (b/a) * (x - h) + k

• y = ± (a/b) * (x - h) + k

• y = ± (a/b) * (x + h) - k

• y = ± (b/a) * (x + h) - k