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Question

# The eccentricity of an ellipse with its centre at the origin is 12. If one of the directrices is x=4, then the equation of the ellipse is

A
4x2+3y2=12
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B
3x2+4y2=12
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C
3x2+4y2=1
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D
4x2+3y2=1
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Solution

## The correct option is B 3x2+4y2=12Equation of directrix is x=4 which is parallel to y-axis so major axis of the ellipse is x-axis and given center of ellipse is origin. Let equation of ellipse be x2a2+y2b2=1(a>b)Given,eccentricity e=12 ,we know that distance of directrix from center is ae=4⟹a=2,from eccentricity definition we get value of b as √3,now equation becomesx24+y23=1⟹3x2+4y2=12

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