Question

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3 2 units, then its eccentricity is :

Answer 1

Answer:

1/3

Step-by-step explanation:

Hi,

If 'a' is the semi major axis of an ellipse,

If 'b' is the semi minor axis of an ellipse,

'e' its eccentricity, then

Length of latus rectum of an ellipse is given by 2b²/a

Distance between the focus and its nearest vertex is a(1-e)

Now, given 2b²/a = 4 and---(1)

a(1-e) = 3/2-----(2)

Dividing (1)/(2), we get

2b²/a²(1-e) = 8/3

But in an ellipse b²/a² = 1 - e²

⇒2(1-e²)/(1-e) = 8/3

⇒ 1 + e = 4/3

⇒ e = 1/3.

Thus the eccentricity of the ellipse is '1/3'

Hope, it helped !