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 given the center, vertex, and focus?

How do you determine whether the major axis of the ellipse is horizontal or vertical?

Given the center at (0,0) and a vertex at (0,9), what is the value of 'a'?

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

How do you derive the final equation of the ellipse from the values of a and b?