Understanding Hyperbolas

The video tutorial explains how to graph a hyperbola from its standard equation. It covers identifying the transverse axis, finding the center, vertices, and foci, and forming a rectangle to sketch asymptotes. The tutorial also derives the equations of the asymptotes and concludes with graphing the hyperbola.

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

• The signs of the terms in the equation

• The values of the denominators

• The order of the terms in the equation

• The coefficients of the equation

How do you find the center of a hyperbola from its equation?

• By identifying the coefficients of x and y

• By solving for x and y

• By using the values inside the squared terms

• By calculating the average of the denominators

What is the significance of the denominators in the hyperbola's equation?

• They represent the squared values of 'a' and 'b'

• They determine the orientation of the hyperbola

• They are used to find the center

• They indicate the direction of the foci

How are the vertices of a hyperbola determined?

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

• By finding the midpoint of the transverse axis

• By using the y-coordinate of the center

• By calculating the average of the foci

What is the length of the conjugate axis in terms of 'b'?

• b^2

• b

• 2b

• b/2

How do you calculate the value of 'c' for the foci?

• c^2 = a^2 + b^2

• c = a - b

• c^2 = a^2 - b^2

• c = a + b

What is the approximate decimal value of the square root of 13?

• 3.5

• 3.8

• 3.6

• 3.7

How do you find the equations of the asymptotes for a hyperbola?

• By finding the midpoint of the foci

• By solving the hyperbola equation

• By using the vertices and the center

• By using the center and the slopes derived from 'a' and 'b'

What is the slope of the asymptotes for a hyperbola with a horizontal transverse axis?

• a and -a

• b and -b

• b/a and -b/a

• a/b and -a/b

What does the graph of a hyperbola look like in relation to its asymptotes?

• It approaches the asymptotes but never touches them

• It is perpendicular to the asymptotes

• It is parallel to the asymptotes

• It intersects the asymptotes