Correct Answer - Option 3 : 18/5
Concept used:
Standard equation of an ellipse, \(\rm\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
If a > b then the length of Latus rectum = \(\rm\frac{2b^2}{a}\)
If b > a then the length of Latus rectum = \(\rm\frac{2a^2}{b}\)
Calculation:
25x2 + 9y2 = 225
⇒ \(\rm\frac{25x^2}{225}+\frac{9y^2}{225}=1\)
⇒ \(\rm\frac{x^2}{9}+\frac{y^2}{25}=1\)
On comparing with std equation a2 = 9, b2 = 25
b > a
⇒ Length of Latus rectum = \(\rm\frac{2a^2}{b}\)
⇒ Length of Latus rectum = (2 × 9)/5 = 18/5
⇒ Length of Latus rectum = 18/5
