Hyperbola Equations and Graphs

The video tutorial explains how to match hyperbola equations to their corresponding graphs by analyzing the transverse axis, center, and distance to vertices. It covers both horizontal and vertical transverse axes, providing examples and standard forms of equations. The tutorial guides viewers through identifying key features of hyperbolas to correctly associate equations with graphs.

What is the first step in matching a hyperbola equation to its graph?

• Find the intercepts on the axes

• Determine the slope of the graph

• Identify the center and transverse axis

• Calculate the area under the curve

Which equation form indicates a horizontal transverse axis?

• Square of y-part plus square of x-part equals 1

• Square of x-part plus square of y-part equals 1

• Square of x-part minus square of y-part equals 1

• Square of y-part minus square of x-part equals 1

For a hyperbola with a horizontal transverse axis, what is the center of the equation x^2/4 - y^2/16 = 1?

• (2, -1)

• (1, 2)

• (2, 1)

• (0, 0)

What indicates a vertical transverse axis in a hyperbola equation?

• Square of y-part minus square of x-part equals 1

• Square of x-part minus square of y-part equals 1

• Square of x-part plus square of y-part equals 1

• Square of y-part plus square of x-part equals 1

What is the center of the hyperbola given by the equation (y+1)^2/16 - (x+2)^2/4 = 1?

• (1, -2)

• (-1, 2)

• (-2, -1)

• (2, 1)

How do you determine the value of A in a hyperbola equation?

• By identifying the intercepts on the axes

• By measuring the area under the curve

• By calculating the distance from the center to the vertices

• By finding the slope of the graph

Which graph matches the equation (x-2)^2/4 - (y-1)^2/16 = 1?

• Graph B

• Graph D

• Graph A

• Graph C

For the equation (y+1)^2/4 - (x+2)^2/16 = 1, what is the distance from the center to the vertices?

• 8 units

• 6 units

• 4 units

• 2 units

Which graph corresponds to the equation (y+1)^2/16 - (x+2)^2/4 = 1?

• Graph A

• Graph C

• Graph B

• Graph D

What is the correct graph for the equation (x-2)^2/16 - (y-1)^2/4 = 1?

• Graph A

• Graph C

• Graph D

• Graph B