Hyperbola Properties and Asymptotes

The video tutorial explains how to write the equation of a hyperbola in standard form and graph it. It covers two examples: one with a horizontal transverse axis and another with a vertical transverse axis. The tutorial details the process of simplifying the equation, plotting the center, vertices, and asymptotes, and sketching the hyperbola. It emphasizes understanding the relationship between the equation's components and the graph's features, such as the transverse and conjugate axes, and the slopes of the asymptotes.

What is the first step in converting the hyperbola equation 9x² - 4y² = 36 into standard form?

• Subtract 36 from both sides

• Add 36 to both sides

• Divide both sides by 36

• Multiply both sides by 36

In the equation x²/4 - y²/9 = 1, what does the '4' represent?

• a²

• c²

• b²

• d²

What is the orientation of the hyperbola with the equation x²/4 - y²/9 = 1?

• Vertical

• Horizontal

• Diagonal

• Circular

How do you determine the slopes of the asymptotes for a hyperbola?

• By using the center coordinates

• By using the rectangle's diagonals

• By using the vertices

• By using the conjugate axis

What is the slope of the asymptote with a positive slope for the hyperbola x²/4 - y²/9 = 1?

• 1/3

• 3/2

• 2/3

• 1/2

In the second example, what does the equation 4y² - x² = 4 indicate about the transverse axis?

• It is circular

• It is diagonal

• It is vertical

• It is horizontal

For the equation y² - x²/4 = 1, what is the value of 'a'?

• 1

• 2

• 3

• 4

What is the center of the hyperbola given by the equation y² - x²/4 = 1?

• (1, 0)

• (0, 1)

• (0, 0)

• (1, 1)

In the second example, what is the slope of the asymptote with a negative slope?

• -3/2

• -2/3

• -1/3

• -1/2

What is the relationship between the vertices and the transverse axis in a hyperbola?

• Vertices are on the asymptotes

• Vertices are at the center

• Vertices are on the transverse axis

• Vertices are on the conjugate axis