Understanding Hyperbolas

The video tutorial explains how to graph a hyperbola using the box method. It starts with understanding the orientation of the hyperbola based on its equation, converting the equation to standard form, and finding the center and vertices. The tutorial then covers calculating the values of a, b, and c using the Pythagorean theorem. It demonstrates how to draw the asymptotes and the hyperbola curve, and concludes with deriving the equations for the asymptotes using the point-slope formula.

What is the first step in writing the equation of a hyperbola in standard form?

• Subtract 64

• Multiply by 64

• Divide by 64

• Add 64

How do you determine the dominant direction of a hyperbola?

• By checking the constant term

• By checking the coefficients

• By checking which term is positive

• By checking which term is negative

What is the center of a hyperbola if no values are added to x or y?

• (0, 0)

• (1, 1)

• (3, 3)

• (2, 2)

If a squared is 16, what is the value of a?

• 3

• 2

• 5

• 4

What is the value of b if b squared is 4?

• 4

• 1

• 2

• 3

How do you find the value of c in a hyperbola?

• a squared minus b squared

• a squared plus b squared

• a times b

• a divided by b

What is the purpose of drawing a rectangle around the vertices and co-vertices?

• To determine the slope

• To calculate the foci

• To draw the asymptotes

• To find the center

What is the slope of the asymptotes if b is 2 and a is 4?

• 2/3

• 1/2

• 3/4

• 1/4

What is the equation of the asymptotes for a hyperbola centered at the origin?

• y = ±1/2x

• y = ±2x

• y = ±3x

• y = x

Which point do both asymptotes of a hyperbola pass through?

• (3, 3)

• (2, 2)

• (0, 0)

• (1, 1)