If the eccentricity and the length of the latus rectum of an ellipse x^2a^2+ y^2b^2=1 are 32 and 1 respectively, then the sum of the lengths of major axis and minor axis of the ellipse is

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Correct answer: A. (a) We have e= 32 and latus rectum =1 ∵2a(1-e^2)=1 ⇒a=2 and b^2=a^2(1-e^2)=4 14=1 ⇒b=1 Sum of major axis and minor axis =2a+2b=6

$If the eccentricity and the length of the latus rectum of an ellipse \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 are \frac{3}{2} and 1 respectively, then the sum of the lengths of major axis and minor axis of the ellipse is$

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