UPSC NDA Math Model Paper 2

Given: Equation of hyperbola is $5 y^{2}-9 x^{2}=36$ The given equation of hyperbola can be re-written as: $\frac{y^{2}}{\frac{36}{5}} - \frac{x^{2}}{4} = 1$ As we can see that, the given hyperbola is a vertical hyperbola. So, by comparing the given equation of hyperbola with $\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1$ we get $\Rightarrow a^{2} = \frac{36}{5}$ and $b^{2}=4$ As we know that, length of latus rectum of a hyperbola is given by $\frac{2 b^{2}}{a}$ So, the length of latus rectum of given hyperbola is $\frac{4 \sqrt{5}}{3}$ units Hence, option A is the correct answer.