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

Question

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

TestHub · Accepted Answer

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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