We plot the vertices:



So we can see that the center is (h,k) = (0,0) and that the hyperbola
must open upward and downward, so the equation is of the form



The transverse axis joins the vertices, so we draw it in green



So "a" is the length of the semi-transverse axis or the distance 
from the center to either vertex, and we see that a = 7

The conjugate axis and the transverse axis bisect each other at
the center, and we are given that the conjugate axis is 18 units,
so we draw it also in green with its midpoint at the center:



Since "b" is the length of the semi-conjugate axis we see that b = 9,
half the given length of the conjugaste axis.

Next we draw the defining rectangle with the ends of the 
transverse and conjugate axes bisecting the sides:



Then we draw the extended diagonals of the defining rectangle,
which are the asymptotes of the hyperbola:




Now we can easily sketch in the hyperbola:




And the equation 



becomes



or



Edwin