Hyperbola Concepts and Properties

The video tutorial explains how to convert an equation into standard form and identify its center, axes, and vertices. It covers the calculation of a, b, and c values, and provides techniques for sketching the graph, including identifying asymptotes and using co-vertices for better graphing accuracy. The tutorial emphasizes understanding the relationship between the graph and its asymptotes, offering practical tips for drawing hyperbolas accurately.

What is the first step in converting the given equation to standard form?

• Multiply both sides by 12

• Divide both sides by 12

• Add 12 to both sides

• Subtract 12 from both sides

After dividing by 12, what does the equation become?

• x^2/4 - y^2/3 = 1

• x^2/3 - y^2/4 = 1

• x^2/3 + y^2/4 = 1

• x^2/4 + y^2/3 = 1

Where is the center of the hyperbola located?

• (1, 1)

• (0, 0)

• (2, 2)

• (-1, -1)

What is the value of a squared in the equation?

• 4

• 3

• 6

• 5

What is the value of b squared in the equation?

• 2

• 5

• 4

• 3

How do you calculate c squared for the hyperbola?

• a^2 * b^2

• b^2 - a^2

• a^2 + b^2

• a^2 - b^2

What is the approximate value of c?

• 2.7

• 2.6

• 2.8

• 2.5

What is the role of the center in the hyperbola?

• It is the origin of the graph

• It is irrelevant

• It is the midpoint of the conjugate axis

• It is the midpoint of the transverse axis

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

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• b^2 - a^2 = c^2

• a^2 * b^2 = c^2

What is the orientation of the transverse axis?

• None

• Vertical

• Diagonal

• Horizontal