Question

Find the eccentricity of the hyperbola the length of whoose conjugate axis is 3/4 of the length of transverse axis

Answer 1

The lengths of the conjugate axis and the transverse axis are 2b and 2a, respectively.
We have:
⇒2b=34×2a⇒b=34a
Using the relation b2=a2(e2−1), we get:

⇒(34)2a2=a2(e2−1)⇒916=e2−1⇒e2=2516⇒e=54
Therefore, the eccentricity of the hyperbola is 54.