Master Writing the equation of a hyperbola given the center is at the origin

The video tutorial explains how to write the equation of a hyperbola given various pieces of information. It covers determining the transverse axis, plotting points, and calculating values for A, B, and C. The tutorial also discusses using both vertical and horizontal transverse axis equations and provides examples to illustrate these concepts.

What is the consistent piece of information given for all hyperbola equations in this tutorial?

• The center is at (0,0).

• The transverse axis is horizontal.

• The foci are at (0,0).

• The vertices are at (0,0).

How do you determine if the transverse axis is vertical or horizontal?

• By checking the position of the center.

• By calculating the value of c.

• By plotting the foci and vertices.

• By measuring the distance between co-vertices.

What is the value of c if the foci are at (0, -6) and (0, 6)?

• 0

• 3

• 6

• 12

Which equation is used when the transverse axis is horizontal?

• y^2/a^2 - x^2/b^2 = 1

• y^2/b^2 - x^2/a^2 = 1

• x^2/a^2 - y^2/b^2 = 1

• x^2/b^2 - y^2/a^2 = 1

If a is sqrt(3), what is a^2?

• 3

• 1.5

• sqrt(3)

• 9

What is the relationship between the co-vertices and the conjugate axis?

• Co-vertices lie on the conjugate axis.

• Co-vertices lie on the transverse axis.

• Co-vertices determine the value of c.

• Co-vertices are at the center.

If b = 5, what is b^2?

• 25

• 15

• 5

• 10

How do you determine the transverse axis when given co-vertices and foci?

• By measuring the distance from the center to the vertices.

• By calculating the midpoint of the co-vertices.

• By checking the distance between the foci.

• By plotting the co-vertices and foci.

What is the value of a^2 if c = 8 and b = 4?

• 32

• 64

• 16

• 48

Which equation is used when the transverse axis is vertical?

• y^2/b^2 - x^2/a^2 = 1

• x^2/b^2 - y^2/a^2 = 1

• y^2/a^2 - x^2/b^2 = 1

• x^2/a^2 - y^2/b^2 = 1