A hyperbola centred at the origin has eccentricity and its transverse axis is units long

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

Problem

A hyperbola centred at the origin has eccentricity

\dfrac{3}{2}

and its transverse axis is

8

units long. Which equation represents this hyperbola? (a)

\dfrac{x^{2}}{20}-\dfrac{y^{2}}{16}=1

(b)

\dfrac{x^{2}}{16}-\dfrac{y^{2}}{36}=1

(c)

\dfrac{x^{2}}{16}-\dfrac{y^{2}}{20}=1

(d)

\dfrac{x^{2}}{64}-\dfrac{y^{2}}{80}=1