Converting to standard form to find the foci, vertices and center of an ellipse

The video tutorial explains how to determine the foci, vertices, and center of an ellipse from its equation. It covers the process of completing the square to transform the equation into standard form, identifies the properties of the ellipse, and calculates its eccentricity. The tutorial emphasizes the differences between horizontal and vertical ellipses and the significance of the major and minor axes.

Describe the steps to rewrite the equation of an ellipse in standard form.

What does it mean if the major axis of an ellipse is horizontal versus vertical?

How do the coordinates of the center of an ellipse relate to its vertices?

What is the eccentricity of an ellipse and how is it calculated?