Hyperbola Properties and Equations

The video tutorial explains how to write the equation of a hyperbola given different pieces of information, focusing on the center at (0,0). It covers the importance of identifying the transverse and conjugate axes, plotting points, and determining the values of a, b, and c. The tutorial also demonstrates using both horizontal and vertical equations for hyperbolas, providing examples and step-by-step calculations.

What is the consistent piece of information given for all hyperbola equations in this tutorial?

• The center is at (0,0)

• The foci are at (0,0)

• The conjugate axis is horizontal

• The vertices are at (0,0)

What lies on the transverse axis of a hyperbola?

• Only the foci

• Co-vertices and center

• Vertices and foci

• Only the center

How can you determine the transverse axis of a hyperbola?

• By plotting the foci

• By plotting the asymptotes

• By plotting the center

• By plotting the co-vertices

What is the value of c if the distance from the center to the foci is 6?

• c = 8

• c = 4

• c = 2

• c = 6

What is the equation used to relate a, b, and c in a hyperbola?

• a^2 = b^2 + c^2

• c^2 = a^2 + b^2

• a^2 + b^2 = c^2

• b^2 = a^2 + c^2

Which equation is used when the transverse axis is horizontal?

• y^2/b^2 - x^2/a^2 = 1

• x^2/b^2 - y^2/a^2 = 1

• x^2/a^2 - y^2/b^2 = 1

• y^2/a^2 - x^2/b^2 = 1

If a is the square root of 3, what is a^2?

• 1

• 2

• 3

• 4

What does the conjugate axis determine in a hyperbola?

• The center of the hyperbola

• The location of the co-vertices

• The location of the foci

• The direction of the transverse axis

In the final example, what is the value of b if the distance from the center to the co-vertices is 4?

• b = 4

• b = 2

• b = 5

• b = 3