5-12 ■ Graphing Shifted Ellipses An equation of an ellipse is given.(a) Find the center, vertices, and foci of the ellipse. (b) Determine the lengths of the major and minor axes. (c) Sketch a graph of the ellipse.
The center, vertices, and foci of the ellipse.
The equation of ellipse is,
The following equation is the basic equation for an ellipse that is not centered at the origin.
With the following properties,
Consider the equation,
Compare the equation of the ellipse with the standard equation.
Calculate the center of the ellipse.
Substitute for and for in equation .
Calculate the vertices of the ellipse.
Substitute for , for and for in equation .
Substitute for , for and for in equation
The length of the major and minor axes.
The graph of the ellipse.
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