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 is the first step in determining the orientation of the transverse axis of a hyperbola?

• Write the equation

• Plot the points

• Determine the center

• Calculate the distance between the foci

When writing the equation of a hyperbola with a horizontal transverse axis, which variable is subtracted from x?

• A

• K

• H

• B

How is the center of a hyperbola determined?

• By adding the coordinates of the foci

• By subtracting the distance from the vertices

• By calculating the average of the foci

• By finding the midpoint between the vertices

What is the value of a if the distance between the vertices is 4?

• 3

• 4

• 2

• 1

What is the relationship between a^2, b^2, and c^2 in a hyperbola?

• a^2 = b^2 + c^2

• c^2 = a^2 + b^2

• b^2 = a^2 - c^2

• a^2 = c^2 - b^2

Why is it important to maintain consistency in calculations when determining the equation of a hyperbola?

• To avoid errors in the distance calculations

• To ensure the equation is in standard form

• To ensure the values of a and b are correct

• To keep the transverse axis horizontal

If c is 3, what is the value of c^2?

• 9

• 12

• 6

• 15