Those two asymptotes are 



Let's check them one by one:

1.The conjugate axis is parallel to the transverse axis.

That is NEVER true for any hyperbola.  The conjugate axis is
always PERPENDICULAR to the the transverse, never parallel. 


2.The vertices are (0,3) and (0,-3).

That could be the case but it is not necessarily true.

It would be true in the case of this hyperbola, 



But not for this one:




3. The hyperbola has only 1 y-intercept.

That CANNOT be true with those asymptotes, because they either
have 2 y-inters


4. There is a focus at (3,5).

That CANNOT be true because with this hyperbola both foci are 
either on the x-axis or the y-axis since the center is at the 
origin. 


5. None of the above are true.

Only 2 COULD BE true, but is certainly not necessarily true.

The problem should NOT have been stated as it was.  #5 should
have had the word "necessarily" inserted.  It should have read:

5. None of the above are NECESSARILY true.

But 5 is the only choice I would select.

Edwin