A) 2/5
B) 3/5
C) 4/5
D) 1/5
Correct Answer: C
Solution :
Given equation of ellipse is, \[25{{x}^{2}}+9{{y}^{2}}-150x-90y+225=0\] \[\Rightarrow \]\[25\,{{(x-3)}^{2}}+9{{(y-5)}^{2}}=225\] \[\Rightarrow \]\[\frac{{{(x-3)}^{2}}}{9}+\frac{{{(y-5)}^{2}}}{25}\] = 1. Here \[b>a\] \[\therefore \] Eccentricity\[e=\sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}=\sqrt{1-\frac{9}{25}}\]\[=\sqrt{\frac{16}{25}}=\frac{4}{5}\].
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