UPSC NDA Math Model Paper 9

The latus rectum =

2b2

a

Half minor axis = b
Given, the latus rectum of an ellipse is equal to half its minor axis.
⇒

2b2

a

=b
⇒

b

a

=

1

2

Now, the eccentricity of ellipse =√1−(

b

a

)2
⇒ Eccentricity of ellipse =√1−

1

4

⇒ Eccentricity of ellipse =

√3

2

Hence, If the latus rectum of an ellipse is equal to half its minor axis, then its eccentricity is

√3

2