obtain the equation of hyperbola in each of the following cases: centre at (0,0) conjugate axis along x-axis of length 6 and eccentricity 2.

Explanation

Here 2b=6 `implies` b=3 , c/a=2 or ca=2
We have `a^2+b^2=c^2` or `a^2+9=4a^2` OR `a^2=3` `therefore` eqn of hyperbola is
`y^2/a^2-x^2/b^2=1 or `y^2/3-x^2/9=1`