Understanding Ellipses: Standard Form and Axes

The video tutorial explains how to find the standard form of an ellipse equation. It begins by identifying the vertical major axis and horizontal minor axis, noting that the center of the ellipse is at the origin. The tutorial then calculates the values of a and b, which represent the distances from the center to the endpoints of the major and minor axes, respectively. Finally, it formulates the standard form equation of the ellipse, considering the center at the origin and the calculated values of a and b.

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

• Vertical

• Horizontal

• None

• Diagonal

Where is the center of the ellipse located?

• At (1, 1)

• At (5, 5)

• At (0, 0)

• At (2, 2)

What is the length of the major axis if a = 5?

• 5

• 20

• 15

• 10

What is the length of the minor axis if b = 2?

• 2

• 4

• 6

• 8

In the standard form of an ellipse with a vertical major axis, where does the larger denominator appear?

• Under both terms

• Under the y-term

• Under the x-term

• It does not matter

What is the value of a^2 if a = 5?

• 15

• 10

• 25

• 20

What is the value of b^2 if b = 2?

• 2

• 8

• 6

• 4

What is the standard form of the ellipse equation derived in the video?

• x^2/4 + y^2/25 = 1

• x^2/25 + y^2/4 = 1

• x^2/5 + y^2/2 = 1

• x^2/2 + y^2/5 = 1

Which axis is longer in the ellipse discussed?

• Minor axis

• Major axis

• Neither

• Both are equal

What is the significance of the center being at the origin for the ellipse equation?

• It changes the axis orientation

• It simplifies the equation

• It complicates the equation

• It has no effect