Understanding Hyperbolas

This video tutorial explains how to graph a hyperbola given its equation in standard form. It covers identifying the transverse axis, finding the center and vertices, determining the conjugate axis, and sketching a rectangle to help draw the asymptotes. The tutorial also includes calculating the foci and deriving the equations of the asymptotes, culminating in graphing the hyperbola by incorporating all these elements.

What determines whether a hyperbola has a vertical or horizontal transverse axis?

• The order of the terms in the equation

• The sign of the coefficients

• The degree of the polynomial

• The presence of a constant term

If the equation of a hyperbola is given as (x+2)^2/16 - (y-3)^2/9 = 1, what is the center of the hyperbola?

• (2, -3)

• (3, -2)

• (-2, 3)

• (-3, 2)

How do you determine the vertices of a hyperbola with a vertical transverse axis?

• By adding and subtracting 'a' from the y-coordinate of the center

• By adding and subtracting 'b' from the x-coordinate of the center

• By adding and subtracting 'b' from the y-coordinate of the center

• By adding and subtracting 'a' from the x-coordinate of the center

What is the length of the conjugate axis if 'b' is 4?

• 2

• 4

• 16

• 8

How can the foci of a hyperbola be found?

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

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

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

• By using the equation c^2 = a^2 * b^2

What is the value of 'c' if a^2 = 9 and b^2 = 16?

• 6

• 5

• 4

• 3

What is the slope of the asymptote with a positive slope for a hyperbola with a = 3 and b = 4?

• 3/4

• -3/4

• -4/3

• 4/3

Which form is used to find the equations of the asymptotes?

• Slope-intercept form

• Point-slope form

• Standard form

• Vertex form

What is the equation of the asymptote with a negative slope if the center is (-2, 3)?

• y + 3 = -3/4(x - 2)

• y - 3 = 3/4(x + 2)

• y - 3 = -3/4(x + 2)

• y + 3 = 3/4(x - 2)

What does the graph of a hyperbola approach?

• The y-axis

• The origin

• The x-axis

• The asymptotes