Find the length of latus rectum of hyperbola 25y² - 24x² = 600 .

Concept: 

Equation of hyperbola , \(\rm \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1\)  

Length of latus rectum, L.R = \(\rm\frac{2b^{2}}{a}\) 

Equation of hyperbola, \(\rm- \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1\) 

Length of latus rectum, L.R = \(\rm\frac{2a^{2}}{b}\)  

Calculation: 

Given equation are ,  25y2 - 24x2 = 600 

⇒ \(\rm- \frac{x^{2}}{25}+\frac{y^{2}}{24}= 1\) 

On comparing with standard equation, a = 5 and b = \(2\sqrt{6}\) 

We know that , length of latus rectum 

L.R = \(\rm\frac{2a^{2}}{b}\) = \(\frac{2\times25}{2\sqrt{6}}\) 

⇒ L.R = \(\frac{25}{\sqrt{6}}\)units .  

The correct option is 1.