Understanding Ellipses

The video tutorial explains how to write the equation of an ellipse in standard form. It covers the identification of major and minor axes, determining the center, and calculating the values of 'a' and 'b' for both vertical and horizontal major axes. The tutorial provides examples to illustrate the process of deriving the standard form equation for ellipses with different orientations of the major axis.

What is the point of intersection of the major and minor axes of an ellipse called?

• Origin

• Center

• Focus

• Vertex

In the equation of an ellipse with a vertical major axis, where is the larger denominator located?

• Under the x-part

• Under the y-part

• Under both parts

• It doesn't matter

If the length of the major axis is 10 units, what is the value of a?

• 3

• 4

• 5

• 6

What is the length of the minor axis if b equals 3?

• 3 units

• 12 units

• 6 units

• 9 units

What is the standard form equation of an ellipse with a vertical major axis and center at (2, -3)?

• (x+2)^2/9 + (y-3)^2/25 = 1

• (x-2)^2/25 + (y+3)^2/9 = 1

• (x+2)^2/25 + (y-3)^2/9 = 1

• (x-2)^2/9 + (y+3)^2/25 = 1

In an ellipse with a horizontal major axis, where is the larger denominator located?

• It doesn't matter

• Under both parts

• Under the y-part

• Under the x-part

What is the center of an ellipse with a horizontal major axis and given as (-4, 5)?

• (5, -4)

• (-4, 5)

• (-5, 4)

• (4, -5)

If the length of the major axis is 12 units, what is the value of a?

• 7

• 6

• 5

• 4

What is the standard form equation of an ellipse with a horizontal major axis and center at (-4, 5)?

• (x-4)^2/36 + (y+5)^2/9 = 1

• (x+4)^2/36 + (y-5)^2/9 = 1

• (x+4)^2/9 + (y-5)^2/36 = 1

• (x-4)^2/9 + (y+5)^2/36 = 1

What is the length of the minor axis if b equals 3 in an ellipse with a horizontal major axis?

• 3 units

• 6 units

• 9 units

• 12 units