How to graph a hyperbola with asymptotes and center at origin

The video tutorial explains how to identify and graph hyperbolas. It begins by distinguishing hyperbolas from ellipses, focusing on the center and the differences in equations. The tutorial then covers calculating the foci and vertices using the formula a^2 + b^2 = c^2. It proceeds to sketch the graph, determine the transverse axis, and find the co-vertices and asymptotes. The video concludes with graphing techniques and tips, emphasizing the use of co-vertices to aid in graphing asymptotes.

What is the center of a hyperbola if the equation is not subtracting anything from x and y?

• (0, 0)

• (1, 1)

• (3, 3)

• (2, 2)

How do you calculate the value of c for the foci of a hyperbola?

• a^2 / b^2 = c^2

• a^2 * b^2 = c^2

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

What is the orientation of the transverse axis if a^2 is under the y term?

• Diagonal

• Vertical

• Circular

• Horizontal

How do you determine the vertices of a hyperbola?

• By adding and subtracting a from the y-coordinate

• By adding and subtracting b from the x-coordinate

• By adding and subtracting b from the y-coordinate

• By adding and subtracting a from the x-coordinate

What is the approximate value of sqrt(13) when estimating the position of the foci?

• Between 5 and 6

• Between 2 and 3

• Between 3 and 4

• Between 4 and 5

What is the equation of the asymptotes for a vertical hyperbola?

• y = ± (a/b)x

• y = ± (b/a)x

• y = ± (a*b)x

• y = ± (a+b)x

How can you use co-vertices to help graph the asymptotes?

• By drawing a triangle

• By creating a circle

• By forming a rectangle

• By making a square