Master determining the center,vertices, foci and aymptotes of a hyperbola center not at origin

This video tutorial explains how to find the center, vertices, foci, and asymptotes of a hyperbola. It covers the differences between hyperbolas, parabolas, and ellipses, focusing on the equations and graphing techniques. The tutorial provides step-by-step instructions on identifying key components like A, B, and C, and demonstrates how to graph hyperbolas, including plotting vertices and foci. It also explains how to calculate asymptotes for both vertical and horizontal transverse axes.

What is the center of a hyperbola typically represented by?

• (H, K)

• (C, D)

• (X, Y)

• (A, B)

In a hyperbola, what does 'A' represent?

• Distance from center to vertices

• Distance from center to foci

• Distance from center to co-vertices

• Distance from center to asymptotes

How do you determine the transverse axis of a hyperbola?

• By the value of C

• By the position of B under X or Y

• By the position of A under X or Y

• By the larger value of A or B

What is the formula for calculating 'C' in a hyperbola?

• C^2 = A^2 - B^2

• C^2 = A^2 + B^2

• C = A + B

• C = A - B

What is the equation for the asymptotes of a hyperbola with a horizontal transverse axis?

• Y = ± (B/A)X

• Y = ± (A/C)X

• Y = ± (A/B)X

• Y = ± (C/A)X

When the transverse axis is vertical, how do you find the vertices?

• Add and subtract A from the X-coordinate

• Add and subtract C from the Y-coordinate

• Add and subtract B from the X-coordinate

• Add and subtract A from the Y-coordinate

In a vertical transverse axis, how are the foci calculated?

• Add and subtract B from the Y-coordinate

• Add and subtract C from the X-coordinate

• Add and subtract C from the Y-coordinate

• Add and subtract A from the X-coordinate

What is the first step in setting up the equation of a hyperbola?

• Divide by the constant to set equal to 1

• Multiply by the constant to set equal to 1

• Add the constant to set equal to 1

• Subtract the constant to set equal to 1

How do you determine the center of a hyperbola from its equation?

• By identifying the values of X and Y

• By identifying the values of A and B

• By identifying the opposite of H and K

• By identifying the opposite of A and B

What is the relationship between the transverse and conjugate axes?

• They are perpendicular and intersect at the center

• They are parallel and intersect at the center

• They are perpendicular and do not intersect

• They are parallel and do not intersect