Conics - Find the formula for a hyperbola

The video tutorial explains how to determine the standard form of a hyperbola. It begins by identifying given points and determining whether the hyperbola is vertical or horizontal. The instructor then explains the formula for a vertical hyperbola and how to calculate the necessary distances and parameters. Finally, the relationship between A, B, and C in hyperbola equations is discussed.

What is the first step in writing the standard form of a hyperbola?

• Plotting the hyperbola on a graph

• Determining the orientation of the transverse axis

• Calculating the distance between foci

• Identifying the center and vertices

How can you determine if a hyperbola's transverse axis is vertical or horizontal?

• By measuring the length of the major axis

• By calculating the area of the hyperbola

• By plotting the given points

• By checking the distance between the foci

What is the formula for a vertical hyperbola?

• (y - k)^2/a^2 - (x - h)^2/b^2 = 1

• (y - k)^2/b^2 - (x - h)^2/a^2 = 1

• (x - h)^2/b^2 - (y - k)^2/a^2 = 1

• (x - h)^2/a^2 - (y - k)^2/b^2 = 1

In a vertical hyperbola, where is 'a' located?

• Under the x-term

• Under the y-term

• Under the c-term

• Under the b-term

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

• a^2 + c^2 = b^2

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

• a^2 = b^2 + c^2

How do you calculate the distance between the center and a vertex of a hyperbola?

• It is equal to b

• It is equal to 2a

• It is equal to a

• It is equal to c

What is the total distance between the two vertices of a hyperbola?

• 2b

• b

• a

• 2a