Understanding Ellipses in Standard Form

The video tutorial explains how to find the equation of an ellipse in standard form. It highlights the importance of identifying the major and minor axes, noting that the major axis is always longer. The center of the ellipse is at the origin, with coordinates (0, 0). The length of the major axis is 2a, and the minor axis is 2b. For the given ellipse, a is 4 and b is 3. The tutorial derives the standard form equation, emphasizing that the larger denominator (a squared) is under the x part of the equation for a horizontal major axis. The final equation is x^2/16 + y^2/9 = 1.

What is the orientation of the major axis in the given ellipse?

• Horizontal

• Vertical

• Diagonal

• None of the above

Where is the center of the ellipse located?

• At (3, 3)

• At (2, 2)

• At (0, 0)

• At (1, 1)

What is the length of the major axis in terms of 'a'?

• a/2

• a

• 4a

• 2a

If 'a' is 4, what is the distance from the center to one endpoint of the major axis?

• 5

• 3

• 2

• 4

What is the length of the minor axis in terms of 'b'?

• b

• 2b

• b/2

• 4b

In the standard form equation of an ellipse, where is a squared placed when the major axis is horizontal?

• Under the x part

• Under both x and y parts

• Not included

• Under the y part

What is the value of b if the distance from the center to one endpoint of the minor axis is 3?

• 1

• 2

• 3

• 4

What is the equation of the ellipse in standard form given a = 4 and b = 3?

• x^2/3 + y^2/4 = 1

• x^2/4 + y^2/3 = 1

• x^2/9 + y^2/16 = 1

• x^2/16 + y^2/9 = 1

What is the value of a squared in the standard form equation if a = 4?

• 20

• 12

• 16

• 8

What is the value of b squared in the standard form equation if b = 3?

• 6

• 9

• 12

• 15