In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :
JEE · Math · previous-year question
- A.$${3 \over 5}$$correct
- B.$${1 \over 2}$$
- C.$${4 \over 5}$$
- D.$${1 \over {\sqrt 5 }}$$
Answer
A. $${3 \over 5}$$
Explanation
$$2ae = 6 \Rightarrow ae = 3;\,\,2b = 8 \Rightarrow b = 4$$ $${b^2} = {a^2}\left( {1 - {e^2}} \right);16 = {a^2} - {a^2}{e^2}$$ $$ \Rightarrow a{}^2 = 16 + 9 = 25$$ $$ \Rightarrow a = 5$$ $$\therefore$$ $$e = {3 \over a} = {3 \over 5}$$
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