Convert to a hyperbola to standard form to find foci, vertices, center and asymptotes

The video tutorial explains how to find the center, vertices, foci, and asymptotes of a hyperbola by first converting the equation into standard form through completing the square. It covers the relationship between A, B, and C in hyperbolas and ellipses, and demonstrates the calculation of these properties step-by-step.

What is the first step in solving the problem of finding the center, vertices, foci, and asymptotes of a hyperbola?

• Rearrange the variables and complete the square

• Directly find the foci

• Calculate the asymptotes

• Solve for the vertices

When completing the square, what must be done to maintain the balance of the equation?

• Multiply both sides by the same value

• Divide both sides by the same value

• Add the same value to both sides

• Subtract the same value from both sides

In a hyperbola, how is the relationship between a, b, and c different from that in an ellipse?

• In a hyperbola, b^2 = a^2 + c^2

• In a hyperbola, c^2 = a^2 + b^2

• In a hyperbola, a^2 = b^2 - c^2

• In a hyperbola, a^2 = b^2 + c^2

What is the center of the hyperbola given in the problem?

• (-2, -3)

• (3, 2)

• (-3, -2)

• (2, 3)

How do you determine the orientation of a hyperbola?

• By the sign of the coefficients

• By the center coordinates

• By the position of a and b in the equation

• By the value of c

What is the formula for the asymptotes of a hyperbola?

• y = k ± (b/a)(x - h)

• y = h ± (a/b)(x - k)

• y = h ± (b/a)(x - k)

• y = k ± (a/b)(x - h)

How are the vertices of a hyperbola determined?

• By adding and subtracting b from the y-coordinate of the center

• By adding and subtracting a from the y-coordinate of the center

• By adding and subtracting c from the x-coordinate of the center

• By adding and subtracting a from the x-coordinate of the center