A) \[\frac{2}{5}\]
B) \[\frac{2}{3}\]
C) \[\frac{4}{5}\]
D) \[\frac{3}{4}\]
E) \[\frac{3}{5}\]
Correct Answer: E
Solution :
The equation of ellipse is \[25{{x}^{2}}+16{{y}^{2}}-150x-175=0\] \[\Rightarrow \]\[25({{x}^{2}}-6x+9)-225+16{{y}^{2}}-175=0\] \[\Rightarrow \] \[\frac{25{{(x-3)}^{2}}}{400}+\frac{16{{y}^{2}}}{400}=0\] \[\Rightarrow \] \[\frac{{{(x-3)}^{2}}}{16}+\frac{{{y}^{2}}}{25}=0\] The major axis of ellipse is a line parallel to y-axis therefore eccentricity of ellipse is given by \[e=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}\]
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