JEE Main · 2006 · 30 Apr 2006 · Offline · Ellipse

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

Answer: (A)

Solution

Let the ellipse have semi-major axis

a

, semi-minor axis

b

and eccentricity

e

. The distance between the foci is

2 a e = 6

, so

a e = 3

, and the minor axis is

2 b = 8

, so

b = 4

. Using

b^{2} = a^{2} (1 - e^{2}) = a^{2} - (a e)^{2}

, we get

16 = a^{2} - 9

, hence

a^{2} = 25

and

a = 5

. The eccentricity is then

e = \frac{a e}{a} = \frac{3}{5}

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option