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Question -

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



Answer -

Given:

We need to find the eccentricity of an ellipse.

(i) Iflatus – rectum is half of its minor axis

We know that the length of the semi – minor axis is b andthe 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

(ii) Iflatus – rectum is half of its major axis

We know that the length of the semi – major axis is a andthe 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

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