Vertices, foci and center of an ellipse in standard form

The video tutorial explains how to determine the properties of an ellipse, including its vertices, center, co-vertices, and foci. It covers the relationship between the major and minor axes and how to calculate the values of A, B, and C. The tutorial emphasizes plotting and visualizing these properties on a graph for better understanding. Several example problems are solved to illustrate the concepts, focusing on the importance of identifying the major and minor axes and their respective properties.

What is the center of an ellipse if the equation is (x + 3)^2/9 + (y + 1)^2/4 = 1?

• (-1, -3)

• (0, 0)

• (3, 1)

• (-3, -1)

In an ellipse, which axis is always longer?

• Major axis

• Minor axis

• Depends on the ellipse

• Both are equal

If a^2 = 9 and b^2 = 4, what is the value of c^2?

• 7

• 3

• 13

• 5

How do you determine the major axis of an ellipse?

• By checking the center

• By comparing a^2 and b^2

• By measuring the distance

• By looking at the coefficients

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

• c^2 = a^2 - b^2

• c = a - b

• c^2 = a^2 + b^2

• c = a + b

When plotting an ellipse, why is it important to identify the major and minor axes?

• To calculate the area

• To find the center

• To identify the foci

• To determine the shape

What is the first step in handling an ellipse equation not set to 1?

• Subtract a constant

• Add a constant

• Divide by the constant on the right

• Multiply by a constant

If the equation of an ellipse is (x - 1)^2/2 + (y + 3)^2/6 = 1, what is the center?

• (0, 0)

• (3, -1)

• (-1, 3)

• (1, -3)

In an ellipse with a vertical major axis, which coordinate changes for the vertices?

• Neither coordinate

• Both coordinates

• Y-coordinate

• X-coordinate

What is the value of a if a^2 = 6?

• sqrt(6)

• 2

• 3

• 6