Standard form of an ellipse when given the focus

The video tutorial explains how to determine the major axis of symmetry for an ellipse, whether it is vertical or horizontal. It discusses the relationship between the foci, center, and vertices, and how they lie on the major axis. The tutorial then derives the standard form of the equation for an ellipse, focusing on calculating the values of A, B, and C. Finally, it demonstrates how to finalize the equation using these calculated values.

What is the first step in determining the major axis of symmetry for an ellipse?

• Identifying the center of the ellipse

• Calculating the length of the minor axis

• Drawing the given foci

• Finding the vertices

In the standard form of an ellipse equation with a horizontal major axis, which variable is associated with the major axis?

• W

• X

• Z

• Y

How is the length of the major axis related to the value of A in an ellipse?

• A is twice the length of the major axis

• A is half the length of the major axis

• A is equal to the length of the major axis

• A is unrelated to the major axis

What is the relationship between C^2, A^2, and B^2 in an ellipse?

• C^2 = A^2 + B^2

• C^2 = A^2 * B^2

• C^2 = B^2 - A^2

• C^2 = A^2 - B^2

What is the value of B^2 if C^2 is 25 and A^2 is 36?

• 11

• 25

• 36

• 61

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

• (1, 1)

• (6, 6)

• (5, 5)

• (0, 0)

What is the final form of the ellipse equation given A = 6 and B^2 = 11?

• X^2/36 + Y^2/11 = 1

• X^2/11 + Y^2/36 = 1

• X^2/6 + Y^2/11 = 1

• X^2/36 + Y^2/6 = 1