Conic Sections Question 377

Question: The eccentricity of the ellipse $ 25x^{2}+16y^{2}=400 $ is

[MP PET 2001]

Options:

A) 3/5

B) 1/3

C) 2/5

D) 1/5

Show Answer

Answer:

Correct Answer: A

Solution:

$ \frac{x^{2}}{16}+\frac{y^{2}}{25}=1 $
$ \Rightarrow a^{2}=b^{2}(1-e^{2}) $

$ \Rightarrow e^{2}=1-\frac{16}{25}\Rightarrow e=3/5 $ .