UPSC NDA Math Model Paper 2

Given: Equation of hyperbola is 5y2−9x2=36
The given equation of hyperbola can be re-written as:

y2

36 5

−

x2

4

=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

5

and b2=4
As we know that, length of latus rectum of a hyperbola is given by

2b2

a

So, the length of latus rectum of given hyperbola is

4√5

3

units
Hence, option A is the correct answer.