For the standard ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with $a>b>0$, which statement is correct?
ATwo ellipses are similar if they have equal major axes
BTwo ellipses are similar if they have equal eccentricity
CTwo ellipses are similar if they have equal latus rectum lengths
DTwo ellipses are similar if they have equal areas
Answer & Solution
Correct answer: B. Two ellipses are similar if they have equal eccentricity
For ellipses, similarity means one can be obtained from the other by uniform scaling. That preserves the ratio $\frac{b}{a}$, and hence preserves eccentricity $e=\sqrt{1-\frac{b^2}{a^2}}$. Therefore equal eccentricity is the correct criterion for similarity.
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