Answer
Foci: $( 1, \pm \sqrt 5 )$
Vertices : $( 1,\pm 3)$
Work Step by Step
$9x^2-18x+4y^2=27$
Rewrite as $\frac{(x-1)^2}{(2)^2}+\frac{y^2}{(3)^2}=1$
$c^2=a^2-b^2=9-4=5$ $c=\sqrt 5$
Foci: $( 1, \pm \sqrt 5 )$
Vertices : $( 1,\pm 3)$