Hyperbola Properties and Calculations

This video tutorial covers the process of graphing two hyperbolas centered at the origin. It explains the differences between horizontal and vertical hyperbolas, focusing on the calculation of vertices, focal points, and asymptotes. The tutorial also highlights the similarities between hyperbolas and ellipses, emphasizing the importance of understanding the equations and their components. By the end, viewers will have a clear understanding of how to graph hyperbolas and the mathematical principles involved.

What is the center of the hyperbolas discussed in the video?

• (0, 0)

• (1, 1)

• (-1, -1)

• (5, 5)

What is the value of 'a' for the horizontal hyperbola?

• 9

• 7

• 5

• 3

What is the value of 'b' for the horizontal hyperbola?

• 3

• 2

• 1

• 4

How do you determine the direction of the hyperbola?

• By the sign of the coefficients

• By the order of x and y

• By the value of b

• By the value of a

What is the formula for calculating c in a hyperbola?

• c = √(a² + b²)

• c = √(a² - b²)

• c = a - b

• c = a + b

What are the coordinates of the vertices for the horizontal hyperbola?

• (-5, 0) and (5, 0)

• (0, -5) and (0, 5)

• (-3, 0) and (3, 0)

• (0, -3) and (0, 3)

What is the approximate value of c for the horizontal hyperbola?

• 4.5

• 5.8

• 6.2

• 7.1

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

• y = -3/5x

• y = -5/3x

• y = 5/3x

• y = 3/5x

What is the equation of the other asymptote for the horizontal hyperbola?

• y = 3/5x

• y = -5/3x

• y = -3/5x

• y = 5/3x

What is the value of 'a' for the vertical hyperbola?

• 3

• 7

• 5

• 9