Prove that for a hyperbola with semi-transverse axis and eccentricity

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that for a hyperbola with semi-transverse axis

a

and eccentricity

e>1

, the length of its semi-conjugate axis is

b=a\sqrt{e^{2}-1}