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 the center, vertex, and focus. It begins by plotting these points and identifying the major axis as vertical. The tutorial then details the formulation of the ellipse equation, focusing on calculating the distances from the center to the vertices and foci. The relationship C^2 = a^2 - B^2 is used to solve for B^2, completing the equation. The process is summarized, emphasizing the importance of understanding the geometric relationships involved.

What is the first step in determining the major axis of an ellipse?

• Determine the length of the major axis

• Calculate the distance between the foci

• Plot the center, vertex, and focus

• Find the midpoint of the vertices

When the major axis of an ellipse is vertical, how is the equation structured?

• (x-h)^2/b^2 + (y-k)^2/a^2 = 1

• (x-h)^2/a^2 - (y-k)^2/b^2 = 1

• (x-h)^2 + (y-k)^2 = 1

• (x-h)^2/a^2 + (y-k)^2/b^2 = 1

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

• The distance from the center to the co-vertices

• The distance between the foci

• The distance from the center to the foci

• The distance from the center to the vertices

Which formula is used to find the value of b^2 in an ellipse?

• b^2 = a^2 + c^2

• b^2 = a^2 - c^2

• b^2 = c^2 - a^2

• b^2 = a^2 * c^2

If the distance from the center to the foci is 6 and a^2 is 64, what is b^2?

• 28

• 72

• 36

• 64