Hyperbola Concepts and Properties

The video tutorial explains how to graph a hyperbola given its standard equation. It covers identifying the type of transverse axis, finding the center, vertices, and endpoints of the conjugate axis. The tutorial also demonstrates sketching asymptotes and calculating the foci, culminating in graphing the hyperbola.

What does the form of the hyperbola equation indicate about the transverse axis?

• It shows whether the axis is horizontal or vertical.

• It determines the color of the graph.

• It specifies the number of vertices.

• It indicates the length of the axis.

Where is the center of the hyperbola located in this example?

• (-1,-1)

• (2,2)

• (0,0)

• (1,1)

What are the coordinates of the vertices of the hyperbola?

• (0,3) and (0,-3)

• (3,0) and (-3,0)

• (0,4) and (0,-4)

• (4,0) and (-4,0)

How do you determine the endpoints of the conjugate axis?

• By moving 'b' units up and down from the center.

• By moving 'a' units up and down from the center.

• By moving 'b' units left and right from the center.

• By moving 'a' units left and right from the center.

What is the purpose of sketching a rectangle on the coordinate plane?

• To calculate the area of the hyperbola.

• To help sketch the asymptotes of the hyperbola.

• To determine the length of the transverse axis.

• To find the center of the hyperbola.

What is the slope of the asymptote with a positive slope?

• 3/4

• 4/3

• -3/4

• -4/3

What is the equation of the asymptote with a negative slope?

• y = -4/3x

• y = 4/3x

• y = -3/4x

• y = 3/4x

How do you calculate the value of 'c' for the foci?

• c^2 = a^2 + b^2

• c^2 = a^2 - b^2

• c = a + b

• c = a - b

What are the coordinates of the foci for this hyperbola?

• (0,4) and (0,-4)

• (5,0) and (-5,0)

• (4,0) and (-4,0)

• (0,5) and (0,-5)

What does the completed graph of the hyperbola include?

• Only the asymptotes.

• The vertices, foci, and asymptotes.

• Only the foci.

• Only the vertices.