Hyperbola Concepts and Equations

The video tutorial explains how to write the equation of a hyperbola given its vertices and asymptotes. It starts by identifying the direction of the hyperbola based on its vertices, then graphs the asymptotes to find the center. The tutorial continues by calculating the values of a and b using the slopes of the asymptotes and concludes by writing the final equation of the hyperbola.

What are the coordinates of the vertices given in the problem?

• (3, 6) and (3, 0)

• (0, 3) and (-6, 3)

• (0, -3) and (6, 3)

• (3, 0) and (3, -6)

Which direction does the hyperbola open based on the given vertices?

• Horizontally

• Diagonally

• Up and down

• Left and right

What is the equation of the first asymptote mentioned?

• y = -x

• x = -y

• x = y

• y = x

Where is the center of the hyperbola located?

• (-3, -3)

• (-3, 3)

• (3, -3)

• (3, 3)

What are the slopes of the asymptotes?

• 2 and -2

• 0 and 1

• 1 and -1

• 3 and -3

What is the value of 'a' in the hyperbola equation?

• 5

• 4

• 3

• 2

What is the value of 'b' in the hyperbola equation?

• 2

• 4

• 5

• 3

What is the formula for the hyperbola with the given center and values of a and b?

• (x-3)^2/9 - (y+3)^2/9 = 1

• (y-3)^2/9 - (x+3)^2/9 = 1

• (x+3)^2/9 - (y-3)^2/9 = 1

• (y+3)^2/9 - (x-3)^2/9 = 1

Why is 'a squared' always placed first in the hyperbola equation?

• Because it represents the horizontal axis

• Because it represents the vertical axis

• Because it is always larger

• Because it is always smaller

What is the final step in determining the equation of the hyperbola?

• Graphing the vertices

• Writing the equation

• Finding the center

• Calculating a and b