Show that the equation of an ellipse can be written as
(b) Use a graphing utility to graph the ellipse
Use the results of part (b) to make a conjecture about the change in the shape of the ellipse as e approaches 0.
To prove: The equation of an ellipse can be re-written in the form of as .
The equation, .
The standard equation of an ellipse is, and eccentricity of the ellipse formulated by the equation .
Consider the standard equation of the ellipse, .
Since, the eccentricity of the ellipse is formulated as,
To graph: The ellipse, for different values of with the use of graphing utility.
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