Q11 of 63 Page 202

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

Equation of an ellipse = , whereas


Length of latus rectum =


Length of minor axis = 2b


So,


{Given}


Ab = 2b2


2b2 – ab = 0


b (2b - a) = 0


So, b = 0 or a = 2b


b2 = a2 (1 - e2)


b2 = (2b)2 (1 - e2)


b2 = 4b2 (1 - e2)





Hence, the eccentricity is .


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