In an ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is

Question

Aicharya · Accepted Answer

Consider the standard equation of the ellipse

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ ,

The distance between it's foci is $6$ , so, $2 c = 6 \Rightarrow c = 3$

and given length of minor axis is $8$ units,

hence, $2 b = 8 \Rightarrow b = 4$

So, the value of $a = \sqrt{b^{2} + c^{2}} = \sqrt{4^{2} + 3^{2}} = 5$

Hence, $e = \frac{c}{a} = \frac{3}{5}$

In an ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then…