Understanding Hyperbolas

This video tutorial introduces hyperbolas, a type of conic section, and explains how to graph them in standard form. It covers the definition of hyperbolas, key features such as vertices, foci, and asymptotes, and provides examples of graphing both horizontal and vertical hyperbolas. The tutorial emphasizes understanding the relationship between the equation components and the graph's features.

What is the defining property of a hyperbola?

• The sum of distances from two fixed points is constant.

• The difference of distances from two fixed points is constant.

• The product of distances from two fixed points is constant.

• The ratio of distances from two fixed points is constant.

Which of the following is NOT a key feature of a hyperbola?

• Foci

• Radius

• Vertices

• Center

How do hyperbolas approach their asymptotes?

• They are perpendicular to the asymptotes.

• They are parallel to the asymptotes.

• They never intersect the asymptotes.

• They intersect the asymptotes.

In the standard form of a hyperbola, what does 'A squared' represent?

• It is always under the positive part of the equation.

• It is always under the sum part of the equation.

• It is always under the product part of the equation.

• It is always under the negative part of the equation.

What is the relationship between A, B, and C in a hyperbola?

• C squared = A squared - B squared

• C squared = A squared + B squared

• C squared = A squared * B squared

• C squared = A squared / B squared

In the example with a horizontal transverse axis, what are the coordinates of the center?

• (2, -3)

• (0, 0)

• (2, 3)

• (4, -3)

For a hyperbola with a horizontal transverse axis, how are the vertices determined?

• By adding and subtracting B from the x-coordinate of the center.

• By adding and subtracting A from the y-coordinate of the center.

• By adding and subtracting A from the x-coordinate of the center.

• By adding and subtracting C from the y-coordinate of the center.

In the example with a vertical transverse axis, what is the value of B?

• 4

• 5

• 2

• 3

How is the rectangle used in graphing a hyperbola?

• It determines the center of the hyperbola.

• It helps in finding the foci of the hyperbola.

• Its diagonals are the asymptotes of the hyperbola.

• It is used to calculate the area of the hyperbola.

In the vertical transverse axis example, what are the coordinates of the center?

• (0, 0)

• (2, 4)

• (2, -4)

• (4, -4)