Circle Problem: The circle x2 + y2 = 25 can be considered an ellipse with major and
Chapter 12, Problem 4(choose chapter or problem)
Circle Problem: The circle x2 + y2 = 25 can be considered an ellipse with major and minor radii equal to each other. a. Find the major and minor radii. b. Based on the Pythagorean property for ellipses, explain why the focal radius of a circle is zero. Where, then, are the foci of a circle? c. The eccentricity of an ellipse is e = where c and a are the focal radius and major radius, respectively. Explain why the eccentricity of a circle is zero. Why is the name eccentricity appropriate in this case? d. The eccentricity of an ellipse is also equal to , where d is the directrix radius. Based on the answer to part c, explain why the directrix of a circle is infinitely far from the center.
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