Ellipse Equations and Graphs

The video tutorial explains how to match graphs of ellipses to their corresponding equations. It begins with a review of the standard form of an ellipse equation, highlighting the significance of the larger denominator in determining the major axis. The tutorial then guides viewers through identifying the center and major axis of each ellipse graph. Finally, it demonstrates how to match each graph with its correct equation by analyzing the center coordinates and the orientation of the major axis.

What is the standard form of an ellipse equation?

• y = mx + b

• ax + by = c

• x^2 + y^2 = r^2

• x^2/a^2 + y^2/b^2 = 1

If the larger denominator is under the x part of the equation, what type of major axis does the ellipse have?

• Diagonal

• None

• Horizontal

• Vertical

What are the coordinates of the center for the first ellipse graph?

• (2, -1)

• (0, 0)

• (1, 2)

• (-2, 1)

Which graph has a center at (-2, 1) and a horizontal major axis?

• Graph C

• Graph A

• Graph D

• Graph B

For the first equation, which graph matches if the center is (2, -1) and the major axis is vertical?

• Graph A

• Graph B

• Graph D

• Graph C

What is the center of the ellipse for the second equation?

• (2, -1)

• (-2, 1)

• (1, 2)

• (0, 0)

Which graph corresponds to the third equation with a center at (2, -1) and a horizontal major axis?

• Graph B

• Graph A

• Graph C

• Graph D

For the last equation, which graph matches if the center is (-2, 1) and the major axis is vertical?

• Graph C

• Graph D

• Graph B

• Graph A

What is the x-coordinate of the center for the third equation?

• 2

• -2

• 0

• 1

Which part of the equation determines the orientation of the major axis?

• The numerator

• The constant term

• The coefficient of x

• The larger denominator