Conic Sections Question 391

Question: The eccentricity of the ellipse $ 25x^{2}+16y^{2}-150x-175=0 $ is

[Kerala (Engg.) 2005]

Options:

A) 2/5

B) 2/3

C) 4/5

D) 3/4

E) 3/5

Show Answer

Answer:

Correct Answer: E

Solution:

$ 25{{(x-3)}^{2}}+16y^{2}=400 $

$ \frac{{{(x-3)}^{2}}}{16}+\frac{y^{2}}{25}=1 $

$ e=\sqrt{1-\frac{16}{25}}=\frac{3}{5} $