Writing the equation of a ellipse given the foci and length of major axis

The video tutorial explains how to plot foci on the major axis of an ellipse, determine the center, and calculate distances to vertices. It covers the selection of the correct equation based on axis orientation and solving for unknowns to finalize the ellipse equation.

What is the significance of plotting the foci on the X-axis?

• It determines the length of the minor axis.

• It indicates the ellipse's orientation.

• It shows the center of the ellipse.

• It helps in identifying the major axis.

How do you find the center of an ellipse given the foci?

• By finding the midpoint of the major axis.

• By averaging the coordinates of the foci.

• By using the length of the minor axis.

• By calculating the distance between the vertices.

What does the variable 'a' represent in the context of an ellipse?

• The length of the minor axis.

• The distance from the center to a vertex.

• The total length of the major axis.

• The distance from the center to a focus.

Which equation is used when the major axis of an ellipse is horizontal?

• x^2/a^2 + y^2/b^2 = 1

• x^2/b^2 + y^2/a^2 = 1

• x^2 + y^2 = 1

• x^2 - y^2 = 1

What is the relationship between C^2, A^2, and B^2 in an ellipse?

• C^2 = A^2 + B^2

• C^2 = A^2 - B^2

• C^2 = B^2 - A^2

• C^2 = A^2 * B^2

Why is it unnecessary to solve for B when finalizing the ellipse equation?

• Because B^2 is directly used in the equation.

• Because B is equal to A.

• Because B is always smaller than A.

• Because B is not part of the ellipse equation.

What is the final form of the ellipse equation derived in the tutorial?

• x^2/21 - y^2/25 = 1

• x^2/25 + y^2/21 = 1

• x^2/21 + y^2/25 = 1

• x^2/25 - y^2/21 = 1