Given: Equation of hyperbola is 3y2−x2=108 The given equation of hyperbola can be re-written as:
y2
36
−
x2
108
=1 As we can see that, the given hyperbola is a vertical hyperbola. So, by comparing the given equation of hyperbola with
y2
a2
−
x2
b2
=1 we get, ⇒a2=36 and b2=108 As we know that, vertices of a vertical hyperbola is given by: (0,±a) So, the vertices of the given hyperbola is: (0,±6) Hence, option C is the correct answer.