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

The video tutorial explains how to write the equation of an ellipse given its center, vertex, and focus. It emphasizes identifying whether the major axis is vertical or horizontal by plotting the given points. The tutorial details the relationship between the vertices, foci, and the center, and how they align on the major axis. It then guides through the process of writing the equation for an ellipse with a vertical major axis, calculating the necessary values for a^2 and b^2, and determining the final equation.

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

• Identify whether the major axis is horizontal or vertical

• Determine the center of the ellipse

• Calculate the area of the ellipse

• Identify the length of the minor axis

How can you determine the orientation of the major axis?

• By checking the length of the minor axis

• By calculating the area of the ellipse

• By analyzing the positions of the vertices, foci, and center

• By measuring the distance between the foci

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

• b^2 = a^2 + c^2

• c^2 = a^2 - b^2

• a^2 = c^2 - b^2

• a^2 = b^2 + c^2

If the center of an ellipse is at (0,0) and the major axis is vertical, where is a^2 placed in the equation?

• Under the x term

• Under the y term

• In the numerator

• It is not used in the equation

What is the value of b^2 if a^2 is 81 and c^2 is 32?

• 49

• 64

• 81

• 32