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

The video tutorial explains how to write the equation of an ellipse given the center, vertex, and co-vertex. It covers determining the major axis orientation, whether horizontal or vertical, and how this affects the placement of 'A' and 'B' in the equation. The tutorial also describes how to graph the ellipse using the given points and explains the significance of 'A' and 'B' as distances from the center to the vertices and co-vertices. Finally, it demonstrates how to write the equation using these components.

What is the first step in writing the equation of an ellipse?

• Determine the type of conic section

• Graph what is known

• Find the length of the major axis

• Calculate the foci

When the major axis of an ellipse is horizontal, where is 'a' placed in the equation?

• Under the Y term

• Above the equation

• Under the X term

• Next to the center

What does 'a' represent in the equation of an ellipse?

• The distance from the center to the co-vertex

• The distance from the center to the vertex

• The distance between the foci

• The length of the minor axis

How do you determine the values of h and k in the ellipse equation?

• By measuring the length of the major axis

• By calculating the midpoint of the vertices

• By using the opposite of the center coordinates

• By using the coordinates of the foci

What is the final form of the ellipse equation given in the video?

• (X - 5)^2 / 4 + (Y + 2)^2 / 25 = 1

• (X + 5)^2 / 4 + (Y - 2)^2 / 25 = 1

• (X - 5)^2 / 25 + (Y + 2)^2 / 4 = 1

• (X + 5)^2 / 25 + (Y - 2)^2 / 4 = 1