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.
Related questions
The points (1, 5), (2, 3) and (minus 2, minus 11) are examined to check whether they are:If three points give an area of zero, what does that show?When the area formula gives a negative value for a triangle, you should:The area of the triangle with vertices (5, 2), (4, 7) and (7, minus 4) is:The area of the triangle with vertices (1, minus 1), (minus 4, 6) and (minus 3, minus 5) iBecause of that, the midpoint of the join of two points is found by:A midpoint divides a line segment in which ratio?The point dividing the join of (4, minus 3) and (8, 5) in the ratio 3 to 1 is: