Write the equation of an ellipse given the foci and major axis length

The video tutorial explains how to derive the equation of an ellipse by plotting given information, identifying the center, foci, and calculating necessary parameters like C, B, and A. It emphasizes the importance of understanding the relationship between these elements and the ellipse's major and minor axes. The tutorial concludes with formulating and verifying the ellipse equation, ensuring the major axis is correctly identified as vertical.

What is the significance of plotting the given information when dealing with ellipses?

• It is used to calculate the area of the ellipse.

• It determines the color of the ellipse.

• It helps in visualizing the ellipse.

• It is necessary for finding the volume of the ellipse.

If the minor axis length is 8, what is the value of B?

• 4

• 2

• 6

• 8

Which formula is used to relate C, a, and B in an ellipse?

• C^2 = a^2 - B^2

• C^2 = a^2 * B^2

• C^2 = a^2 + B^2

• C^2 = a^2 / B^2

Why is it important to know if the major axis is vertical or horizontal?

• To calculate the area of the ellipse.

• To decide the orientation of the ellipse.

• To determine the color of the ellipse.

• To find the volume of the ellipse.

What is the final equation of the ellipse given in the tutorial?

• (X + 2)^2 / 25 + (Y - 1)^2 / 16 = 1

• (X - 2)^2 / 16 + (Y + 1)^2 / 25 = 1

• (X - 2)^2 / 25 + (Y + 1)^2 / 16 = 1

• (X + 2)^2 / 16 + (Y - 1)^2 / 25 = 1