In the ellipse, the distance between its foci is 6 and minor axis is 8.

Question

In the ellipse, the distance between its foci is $6$ and minor axis is $8$. Then its eccentricity is :

Accepted Answer

$$2ae = 6 \Rightarrow ae = 3;\,\,2b = 8 \Rightarrow b = 4$$

$${b^2} = {a^2}\left( {1 - {e^2}} \right);16 = {a^2} - {a^2}{e^2}$$

$$ \Rightarrow a{}^2 = 16 + 9 = 25$$

$$ \Rightarrow a = 5$$

$$\therefore$$ $$e = {3 \over a} = {3 \over 5}$$

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