Find the eccentricity of the hyperbola, the length of whose conjugate axis is34 of the length of transverse asxis.
Let 2a and 2b be the transverse and conjugate axes and e be the eccentricit.
Then,
The length of conjugate aaxis=34[length of transverse axis]
⇒2b=34×(2a)
⇒ba=34
⇒b2a2=916
Now,using the relation
e=√1+b2a2
=√1+916
=√2516
=54
Hence,e=54