How to write the equation of an ellipse given the center, focus and co vertex

The video tutorial explains how to write the equation of an ellipse when given the center, focus, and vertex. It begins by determining whether the major axis is horizontal or vertical, which influences the form of the equation. The instructor plots the center, focus, and co-vertex to identify the major axis. The tutorial then derives the equation for a horizontal major axis and substitutes known values. Finally, it solves for unknowns using the relationship between the center, vertices, and foci.

What is the significance of identifying whether the major axis of an ellipse is horizontal or vertical?

• It determines the color of the ellipse.

• It helps in deciding the type of equation to write.

• It affects the size of the ellipse.

• It changes the number of foci.

Which elements lie on the major axis of an ellipse?

• Vertices, foci, and center

• Co-vertices and center

• Only the center

• Only the foci

In the equation of an ellipse with a horizontal major axis, what does 'a' represent?

• The distance from the center to the origin

• The distance from the center to the co-vertices

• The distance from the center to the vertices

• The distance from the center to the foci

What is the relationship between 'a', 'b', and 'c' in the context of an ellipse?

• a^2 = b^2 + c^2

• c^2 = a^2 + b^2

• c^2 = a^2 - b^2

• a^2 = c^2 - b^2

If the distance from the center to the foci is 5 and b^2 is 4, what is a^2?

• 21

• 9

• 25

• 29