Ellipse Properties and Equations

The video tutorial explains how to graph an ellipse that is not centered at the origin. It begins with the equation of the ellipse and defines the values of a, b, and c, which represent distances from the center to the vertices, co-vertices, and foci, respectively. The tutorial then guides viewers through plotting the ellipse on a graph, identifying the center, vertices, co-vertices, and foci. It concludes with calculating the lengths of the major and minor axes, providing a comprehensive understanding of graphing ellipses.

What is the equation of the ellipse discussed in the video?

• (x + 3)^2/25 + (y - 2)^2/9 = 1

• (x - 3)^2/9 + (y + 2)^2/25 = 1

• (x - 3)^2/25 + (y + 2)^2/9 = 1

• (x + 3)^2/9 + (y - 2)^2/25 = 1

How is the value of 'a' determined from the equation?

• a is the sum of the denominators

• a is the square root of the smaller denominator

• a is the square root of the larger denominator

• a is the difference of the denominators

What is the value of 'c' in the ellipse equation?

• 6

• 5

• 4

• 3

Where is the center of the ellipse located?

• (3, -2)

• (3, 2)

• (-3, 2)

• (-3, -2)

In which direction do the vertices of the ellipse lie?

• Randomly

• Diagonal

• Along the y-axis

• Along the x-axis

What are the coordinates of the vertices?

• (3, 3) and (3, -7)

• (3, 5) and (3, -5)

• (3, 7) and (3, -7)

• (3, 2) and (3, -2)

How are the co-vertices of the ellipse determined?

• By moving up and down from the center

• By moving randomly from the center

• By moving left and right from the center

• By moving diagonally from the center

What is the length of the major axis?

• 5

• 6

• 10

• 12

What is the length of the minor axis?

• 12

• 9

• 6

• 3

How is the length of the major axis calculated?

• 2 times the value of b

• 2 times the value of a

• The difference of a and b

• The sum of a and b