Understanding Hyperbolas

This video tutorial focuses on hyperbolas, covering their equations, graphing techniques, and key features such as vertices, foci, and asymptotes. It explains the differences between horizontal and vertical hyperbolas, how to graph them, and how to determine their domain and range. The tutorial also discusses the equations for hyperbolas not centered at the origin and provides examples to illustrate these concepts.

What is the equation of a horizontal hyperbola centered at the origin?

• x^2/a^2 + y^2/b^2 = 1

• x^2/a^2 - y^2/b^2 = 1

• y^2/a^2 - x^2/b^2 = 1

• x^2/b^2 - y^2/a^2 = 1

In a hyperbola, what is the relationship between a, b, and c?

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

• c^2 = b^2 - a^2

• c^2 = a^2 * b^2

What is the length of the transverse axis in a hyperbola?

• a

• b

• 2a

• 2b

For a horizontal hyperbola centered at the origin, what is the equation of the asymptotes?

• y = ±(a/b)x

• x = ±(a/b)y

• y = ±(b/a)x

• x = ±(b/a)y

If a hyperbola is not centered at the origin, how does the equation change?

• (x-h)^2/b^2 - (y-k)^2/a^2 = 1

• (x-h)^2/a^2 - (y-k)^2/b^2 = 1

• x^2/a^2 + y^2/b^2 = 1

• x^2/a^2 - y^2/b^2 = 1

In the example, what is the value of c if a^2 = 16 and b^2 = 9?

• 3

• 6

• 4

• 5

What is the domain of a vertical hyperbola?

• All real numbers

• x > 0

• x < 0

• x ≠ 0

How do you find the new vertices of a hyperbola when it is not centered at the origin?

• Multiply the center coordinates by the original vertices

• Divide the center coordinates by the original vertices

• Subtract the center coordinates from the original vertices

• Add the center coordinates to the original vertices

What is the equation for the asymptotes of a vertical hyperbola not centered at the origin?

• y - k = ±(a/b)(x - h)

• y - k = ±(b/a)(x - h)

• x - h = ±(a/b)(y - k)

• x - h = ±(b/a)(y - k)

What is the range of a vertical hyperbola?

• y < 0

• y > 0

• All real numbers

• y ≠ 0