The Eccentric Ellipse
If the eccentricity of a certain ellipse is equivalent to the ratio of its semi-minor axis to its semi-major axis, then the eccentricity is where is an integer. Find .
The answer is 2.
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1 solution
Let the semi-minor axis be b and the semi-major axis be a. Then eccentricity e is given by e^2=1-(b/a)^2=(b/a)^2 (given). Therefore b/a=1/√2, and e=1/√2