question_answer

In an ellipse the distance between its foci is 6 and length of its minor axis is 8. Then Its eccentricity is:

A) (a) \[\frac{5}{3}\]                      

B) (b) \[\frac{1}{2}\]                

C) (c) \[\frac{3}{5}\]                                  

D) (d) \[\frac{3}{4}\]

Correct Answer: C

Solution :

[c] \[\because 2ae=6\] \[\Rightarrow ae=3\]                             ................(1) \[\because 2b=8\] \[b=4\] \[\because {{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] \[{{(4)}^{2}}={{a}^{2}}-{{a}^{2}}{{e}^{2}}\] \[16+9={{a}^{2}}\] \[\Rightarrow a=5\] \[\therefore ae=3\] \[\because e=\frac{3}{a}=\frac{3}{5}\]Hence, option [c] is correct.