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

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Please find below the solution to the asked query:

We have, latus rectum of an ellipse is equal to half the minor axisconsidering the equation of ellipse as,x2a2+y2b2=1length of latus rectum=2b2alength of minor axis=2bAccording to question,2b2a=b⇒2b2 - ab = 0⇒b2b - a = 0⇒a = 2b   as, b≠0eccentricity, e=1-b2a2=1-b24b2=1-14=34=32

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length of letus rectum = 2b2/a,
length of minor axis = 2b,
equation of eccentricity = square root under a2-b2/a2,
also given that 2b2/a = b.
2b=a ,
put value in the equation of eccentricity and replace a by 2b ,
we get eccentricity = square root under 4b2-b2/4b2 = square root under 3/4
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