Question 1033592
The length of conjugate axis = 2b = 2 ==> b = 1.

The hyperbola would take the form {{{y^2/a^2 - x^2/b^2 = 1}}}

==> {{{y^2/a^2 - x^2/1^2 = 1}}}, or {{{y^2/a^2 - x^2 = 1}}}

For a hyperbola, {{{c^2 = a^2 + b^2}}} ==> {{{(3*sqrt(2))^2 = a^2 +1}}}

==> {{{18 = a^2 + 1}}}  ==> {{{a^2 = 17}}}

Therefore the equation of the hyperbola is {{{y^2/17 - x^2 = 1}}}.