UPSC NDA Math Model Paper 9

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.