Understanding Ellipses

This video tutorial explains how to graph an ellipse when its center is not at the origin. It covers identifying the major and minor axes by examining the equation's denominators, finding the center coordinates, plotting the endpoints of the axes, calculating and plotting the foci, and determining the ellipse's eccentricity. The tutorial provides step-by-step instructions and uses examples to illustrate each concept, ensuring a comprehensive understanding of ellipse graphing.

What is the major axis of an ellipse when the larger denominator is under the x part of the equation?

• Diagonal

• Horizontal

• None

• Vertical

If the equation of an ellipse is in the form (x + 3)^2/a^2 + (y - 2)^2/b^2 = 1, what are the coordinates of the center?

• (3, 2)

• (-3, -2)

• (-3, 2)

• (3, -2)

How do you determine the endpoints of the major axis for an ellipse with a horizontal major axis?

• a units above and below the center

• a units to the right and left of the center

• b units above and below the center

• b units to the right and left of the center

What are the coordinates of the endpoints of the minor axis if b = 3 and the center is at (-3, 2)?

• (-3, 3) and (-3, -3)

• (-3, 0) and (-3, 6)

• (-3, 1) and (-3, -5)

• (-3, -1) and (-3, 5)

Which equation is used to find the value of c for the foci of an ellipse?

• c^2 = a^2 - b^2

• b^2 = a^2 + c^2

• c^2 = a^2 + b^2

• a^2 = b^2 + c^2

What is the approximate value of c if a^2 = 16 and b^2 = 9?

• 2.646

• 1.732

• 4.000

• 3.000

How is the eccentricity of an ellipse calculated?

• a divided by c

• b divided by a

• c divided by a

• a divided by b

What is the eccentricity of an ellipse if c = √7 and a = 4?

• 0.661

• 0.707

• 0.500

• 0.750

What does an eccentricity closer to zero indicate about the shape of an ellipse?

• More elongated

• More circular

• More rectangular

• More triangular

What is the length of the major axis if a = 4?

• 4 units

• 8 units

• 16 units

• 2 units