Master How to determine the vertices, foci and asymptotes of a hyperbola center at origin

The video tutorial explains how to determine the vertices, asymptotes, and foci of a hyperbola. It highlights the differences between hyperbolas and ellipses, particularly in their equations and relationships between A, B, and C. The tutorial provides step-by-step instructions on graphing hyperbolas, identifying the center, and calculating distances to vertices and foci. It also covers the use of co-vertices and asymptotes in graphing.

What is the main difference between the equations of a hyperbola and an ellipse?

• Hyperbolas have a subtraction between terms, while ellipses have addition.

• Ellipses have a subtraction between terms, while hyperbolas have addition.

• Both have addition between terms.

• Both have subtraction between terms.

In a hyperbola, what does the variable 'a' represent?

• Distance from the center to the asymptotes

• Distance from the center to the vertices

• Distance from the center to the Co vertices

• Distance from the center to the foci

How do you determine the center of a hyperbola?

• By finding the midpoint of the vertices

• By using the intersection of the asymptotes

• By using the midpoint of the foci

• By setting the equation equal to zero

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 = a^2 - b^2

When graphing a hyperbola, what is the purpose of the Co vertices?

• They are points on the hyperbola.

• They are used to calculate the foci.

• They help in determining the asymptotes.

• They are used to find the center.

How do you find the asymptotes of a hyperbola?

• By using the formula y = ± (c/a)x

• By using the formula y = ± (a/b)x

• By using the formula y = ± (b/a)x

• By using the formula y = ± (a/c)x

In the example problem, what is the value of 'c' if a^2 = 16 and b^2 = 25?

• c = sqrt(16)

• c = sqrt(41)

• c = 5

• c = 7

What is the first step in solving a hyperbola equation that is not equal to 1?

• Subtract the constant from both sides

• Add the constant to both sides

• Divide both sides by the constant

• Multiply both sides by the denominator

In the final example, what is the simplified form of the equation y^2/32 - x^2/16 = 1?

• y^2/4 - x^2/2 = 1

• y^2/8 - x^2/4 = 1

• y^2/32 - x^2/16 = 1

• y^2/16 - x^2/8 = 1

What is the slope of the asymptotes in the final example problem?

• ± 3/4

• ± 1/2

• ± 2

• ± sqrt(2)