Given an equation find the vertices, center and foci of hyperbola

Why is it important to divide the hyperbola equation by a constant to make it equal to 1?

• To simplify the equation

• To make the equation easier to solve

• To ensure the equation is in standard form

• To eliminate fractions

What does the center of a hyperbola represent in its equation?

• The midpoint of the conjugate axis

• The point where the graph intersects the y-axis

• The midpoint of the transverse axis

• The point where the graph intersects the x-axis

How can you determine if the transverse axis of a hyperbola is horizontal?

• If the x-term is first in the equation

• If the y-term is first in the equation

• If the equation has no fractions

• If the equation is equal to zero

What is the relationship between 'a' and the vertices of a hyperbola?

• 'a' is the distance from the center to the asymptotes

• 'a' is the distance from the center to the co-vertices

• 'a' is the distance from the center to the foci

• 'a' is the distance from the center to the vertices

How do you calculate the foci of a hyperbola?

• By using the formula c^2 = a^2 + b^2

• By adding and subtracting 'a' from the center

• By using the formula c^2 = a^2 - b^2

• By adding and subtracting 'b' from the center

What is the approximate value of sqrt(13) used for estimating the foci?

• 3.5

• 2.5

• 4.0

• 3.0

Why is it helpful to plot the graph of a hyperbola even if not required?

• To check for errors in calculations

• To determine the slope of the asymptotes

• To find the exact values of the foci

• To visualize the relationship between the center, vertices, and foci