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The eccentricity of an ellipse, with its centre at the origin, is 1 2 . If one of the directrices is x= 4 , then the equation of the ellipse is

Options

A3 x^2+4 y^2=1
B3 x^2+4 y^2=12
C4 x^2+3 y^2=12
D4 x^2+3 y^2=1

Correct answer

B. 3 x^2+4 y^2=12

Step-by-step solution

Equation of directrix is x=a / e=4 a=2 b^2=a^2 (1-e^2 ) b^2=3 Hence equation of ellipse is 3 x^2+4 y^2=12

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