Hyperbola Properties and Equations

The video tutorial explains how to find the standard equation of a hyperbola given its center, focus, and vertex. It covers plotting these points on a coordinate plane, identifying the transverse and conjugate axes, and calculating the necessary parameters 'a', 'b', and 'c'. The tutorial then derives the standard equation and demonstrates how to graph the hyperbola, including sketching its asymptotes.

What are the coordinates of the center of the hyperbola?

• (0, 0)

• (-5, 2)

• (-6, 2)

• (-1, 2)

How many units is the focus from the center?

• 3 units

• 6 units

• 4 units

• 5 units

What type of transverse axis does the hyperbola have?

• Horizontal

• Diagonal

• None

• Vertical

Which part of the equation comes first for a horizontal transverse axis?

• W part

• Z part

• X part

• Y part

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

• 5

• 4

• 3

• 6

What is the relationship between a, b, and c 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

What is the value of b squared in this hyperbola?

• 25

• 36

• 16

• 9

What is the final equation of the hyperbola?

• (x + 1)^2/9 + (y - 2)^2/16 = 1

• (x - 1)^2/16 + (y - 2)^2/9 = 1

• (x - 1)^2/9 - (y + 2)^2/16 = 1

• (x + 1)^2/16 - (y - 2)^2/9 = 1

What is the purpose of forming a rectangle when graphing the hyperbola?

• To find the center

• To determine the foci

• To calculate the vertices

• To sketch the asymptotes

How does the hyperbola relate to the asymptotes?

• It intersects them

• It approaches them

• It is parallel to them

• It is perpendicular to them