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$Ratio of the greatest and least focal distances of a point on the ellipse 4 x^{2} + 9 y^{2} = 36 is$

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Correct option is A

Ellipse x29+y24=1(a>b)a2=9,b2=4,e=a2−b2a2=9−49=53 Greatest focal distance =a+ae Least focal distance =a−ae∴ Required ratio =a+aea−ae=1+e1−e=1+531−53=3+53−5=(3+5)24=7+352

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Ratio of the greatest and least focal distances of a point on the ellipse 4x2+9y2=36 is

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$Ratio of the greatest and least focal distances of a point on the ellipse 4 x^{2} + 9 y^{2} = 36 is$