How to graph an ellipse with the center at the origin

The video tutorial explains how to graph an ellipse by identifying key components such as the center, vertices, and foci. It begins with understanding the equation of the ellipse and determining the largest denominator to find a^2 and b^2. The center is identified as (0,0) since the equation lacks h and k values. The tutorial then explains how to find the vertices and foci by determining the major axis, which is horizontal in this case. Finally, the video demonstrates plotting the ellipse and labeling the center, vertices, co-vertices, and foci.

What is the first step in identifying the components of an ellipse from its equation?

• Calculating the center

• Finding the value of c^2

• Identifying the largest denominator

• Determining the foci

How do you calculate c^2 for an ellipse?

• c^2 = a^2 * b^2

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

• c^2 = a^2 / b^2

What is the center of the ellipse given the equation x^2/16 + y^2/4 = 1?

• (1, 1)

• (0, 0)

• (4, 2)

• (16, 4)

How do you determine the major axis of an ellipse?

• By the center coordinates

• By the position of a^2 under x or y

• By the value of b

• By the value of c

If a^2 is under the x variable, what is the orientation of the major axis?

• Horizontal

• Circular

• Vertical

• Diagonal

What is the distance used to determine the position of the foci?

• c

• d

• b

• a

What is the approximate value of c if c^2 = 12?

• 4

• 3

• 2√3

• 2