Question

find the eccentricity of the ellipse 25x^2+16y^2=1600

Answer 1

$\frac{ {x}^{2} }{64} + \frac{ {y}^{2} }{100} = 1$
$e = \sqrt{1 - \frac{ {b}^{2} }{ {a}^{2} } }$
$= \sqrt{1 - \frac{64}{100} }$
$= \sqrt{ \frac{36}{100} }$
$= \frac{6}{10}$
$= \frac{3}{5}$