When given the asymptotes and vertices, find the equation of the hyperbola

The video tutorial guides viewers through writing the equation of a hyperbola. It begins by identifying the type of hyperbola equation needed, then moves on to plotting the vertices and determining the transverse axis. The instructor explains how to find the center and use asymptotes to finalize the equation. The tutorial concludes with the complete hyperbola equation, emphasizing the importance of understanding the relationship between the vertices, center, and asymptotes.

What is the first step in writing the equation of a hyperbola?

• Decide if the hyperbola is horizontal or vertical

• Identify the center of the hyperbola

• Calculate the distance between the foci

• Determine the type of conic section

How do you find the center of a hyperbola given its vertices?

• Use the midpoint formula

• Find the intersection of the asymptotes

• Use the distance formula

• Calculate the average of the foci

What is the value of 'a' if the distance from the center to a vertex is 5?

• 10

• 2.5

• 15

• 5

Which formula is used to find 'b' when given the asymptote of a hyperbola?

• b = a / slope of asymptote

• b = c / a

• b = a / c

• b = a * c

What is the final form of the hyperbola equation if a^2 = 25 and b^2 = 9?

• (x^2/25) - (y^2/9) = 1

• (y^2/9) - (x^2/25) = 1

• (x^2/9) - (y^2/25) = 1

• (y^2/25) - (x^2/9) = 1