Master how to write the equation of an ellipse when the center is not at the origin

The video tutorial explains how to write the equation of an ellipse when the center is not at the origin. It covers plotting given information, identifying key parameters like a and b, and using these to solve for the ellipse equation. The tutorial also demonstrates determining the center and axes orientation, and finalizing the equation with calculated values.

What is the first step in writing the equation of an ellipse when the center is not at the origin?

• Calculate the midpoint

• Plot the given information

• Identify the lengths of the axes

• Determine the orientation of the axes

How do you determine which formula to use for the equation of an ellipse?

• By the position of the center

• By whether the major axis is vertical or horizontal

• By the distance between the vertices

• By the length of the major axis

If the length of the major axis is 10, what is the value of 'a'?

• 10

• 5

• 2

• 20

What is the relationship between the length of the major axis and 'a'?

• The major axis is equal to 'a'

• The major axis is half of 'a'

• The major axis is the square of 'a'

• The major axis is twice 'a'

How can you find the center of an ellipse if only the endpoints of the axes are given?

• By calculating the average of the endpoints

• By using the midpoint formula

• By measuring the distance between endpoints

• By plotting the endpoints and guessing

What is the significance of the midpoint in determining the center of an ellipse?

• It is the intersection of the major and minor axes

• It is the average of the vertices

• It is the shortest distance from the center

• It is the longest distance from the center

When given the endpoints of the major and minor axes, what is the first step to find the center?

• Calculate the distance between endpoints

• Use the midpoint formula

• Plot the endpoints

• Determine the length of the axes