Question

Find the eccentricity of an ellipse whose latus – rectum is
(i) Half of its minor axis
(ii) Half of its major axis

Answer 1

Given:

We need to find the eccentricity of an ellipse.

(i) If latus – rectum is half of its minor axis

We know that the length of the semi – minor axis is b and the length of the latus – rectum is 2b²/a.

2b²/a = b

a = 2b …. (1)

By using the formula,

We know that eccentricity of an ellipse is given as

From equation (1)

(ii) If latus – rectum is half of its major axis

We know that the length of the semi – major axis is a and the length of the latus – rectum is 2b²/a.

2b²/a

a² = 2b² …. (1)

By using the formula,

We know that eccentricity of an ellipse is given as

From equation (1)