Understanding Hyperbolas

This video tutorial covers the formulas and graphing techniques for hyperbolas, including those centered at the origin and those with non-origin centers. It explains key components such as vertices, asymptotes, and foci, and provides example problems to illustrate these concepts. The tutorial emphasizes the importance of understanding the order of terms in the formulas and how they affect the graph's orientation.

What is the direction of a hyperbola that has the equation x²/a² - y²/b² = 1?

• Opens left and right

• Opens up and down

• Forms a circle

• Forms an ellipse

What is the name of the rectangle used in graphing hyperbolas?

• Fundamental Rectangle

• Asymptotic Rectangle

• Vertex Rectangle

• Central Rectangle

In the equation of a hyperbola, what are the points called where the hyperbola intersects its transverse axis?

• Centers

• Asymptotes

• Vertices

• Foci

How do you determine the center of a hyperbola with the equation (x-h)²/a² - (y-k)²/b² = 1?

• (x, y)

• (0, 0)

• (a, b)

• (h, k)

What is the relationship between a, b, and c in a hyperbola?

• c² = a² + b²

• c² = a² - b²

• c² = a² * b²

• c² = a² / b²

In a hyperbola, what is the term for the line that the hyperbola approaches but never touches?

• Axis

• Vertex

• Focus

• Asymptote

For a hyperbola centered at (h, k), which equation represents the asymptotes?

• y = ±(b/a)(x+k) - h

• y = ±(a/b)(x-h) + k

• y = ±(a/b)(x+k) - h

• y = ±(b/a)(x-h) + k

In the example problem, what is the value of 'a' if the equation is x²/4 - y²/9 = 1?

• 9

• 4

• 3

• 2

What is the domain of the hyperbola in the example problem x²/4 - y²/9 = 1?

• (-2, 2)

• (-∞, -2] ∪ [2, ∞)

• [0, ∞)

• (-∞, ∞)

In the example problem, what is the range of the hyperbola x²/4 - y²/9 = 1?

• (-3, 3)

• (-∞, -3] ∪ [3, ∞)

• (-∞, ∞)

• [0, ∞)