Given a formula of hyperbola in standard form find foci, asymptotes, center vertices

The video tutorial explains how to solve a hyperbola problem by determining its orientation, finding the center, vertices, foci, and asymptotes, and finally sketching the graph. The teacher guides through the process of identifying whether the hyperbola is vertical or horizontal, calculating the necessary components using formulas, and plotting the graph accurately.

What is the first step in solving the given hyperbola problem?

• Finding the asymptotes

• Identifying the type of conic section

• Calculating the foci

• Determining the center of the hyperbola

Which formula is used for a vertical hyperbola?

• (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

• (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1

• (x - h)^2 / b^2 - (y - k)^2 / a^2 = 1

• (y - k)^2 / b^2 - (x - h)^2 / a^2 = 1

What are the values of a^2 and b^2 for the given hyperbola?

• a^2 = 64, b^2 = 49

• a^2 = 49, b^2 = 64

• a^2 = 25, b^2 = 81

• a^2 = 81, b^2 = 25

How is the center of the hyperbola determined?

• By calculating the distance between the foci

• By using the formula c^2 = a^2 + b^2

• By setting h and k to zero

• By finding the midpoint of the vertices

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

• c^2 = a^2 * b^2

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

• c^2 = b^2 - a^2

What is the formula for the asymptotes of a hyperbola?

• y = h ± (b/a)(x - k)

• y = k ± (a/b)(x - h)

• y = k ± (b/a)(x - h)

• y = h ± (a/b)(x - k)

What is the approximate value of the foci for the given hyperbola?

• 12

• 5

• 10.29

• 9