Two ellipses have the same eccentricity and their semi-major axes are and respectively

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Two ellipses have the same eccentricity

e

and their semi-major axes are

a

and

2a

respectively. How does the length of the semi-minor axis of the second ellipse compare with that of the first? (a) It becomes

\sqrt{2}

times (b) It is double (c) It is unchanged (d) It is half