Graph an ellipse with the center not at the origin

The video tutorial explains the transition from a circle equation to an ellipse equation, highlighting the differences in coefficients. It covers algebraic manipulation to convert the equation, finding the center, and graphing the ellipse. The tutorial also discusses identifying the major and minor axes, calculating vertices, co-vertices, and foci, emphasizing the importance of understanding these concepts for graphing ellipses.

What is the key difference in the coefficients that helps identify an ellipse from a circle?

• The coefficients are equal in an ellipse.

• The coefficients are different in a circle.

• The coefficients are equal in a circle.

• The coefficients are different in an ellipse.

What is the value of a^2 in the given ellipse problem?

• 4

• 2

• 1/4

• 1/2

How is the center of the ellipse determined?

• By calculating the average of the vertices.

• By finding the midpoint of the major axis.

• By using the midpoint of the minor axis.

• By using the opposite of H and K values.

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

• None of the above

• Vertical

• Diagonal

• Horizontal

How are the vertices of the ellipse determined?

• By moving a distance of a from the center along the minor axis.

• By moving a distance of c from the center.

• By moving a distance of a from the center along the major axis.

• By moving a distance of b from the center.

What is the role of the foci in the ellipse?

• They determine the length of the minor axis.

• They lie on the minor axis.

• They lie on the major axis and help define the ellipse's shape.

• They are the midpoint of the ellipse.

How are the co-vertices of the ellipse calculated?

• By moving a distance of b from the center along the minor axis.

• By moving a distance of a from the center along the major axis.

• By moving a distance of c from the center.

• By moving a distance of b from the center along the major axis.