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An ellipse has eccentricity 1/2 and one...

An ellipse has eccentricity `1/2` and one focus at the point `P(1/2,1)`. Its one directrix is the comionand tangent nearer to the point the P to the hyperbolaof `x^2-y^2=1` and the circle `x^2+y^2=1`.Find the equation of the ellipse.

A

`9(x-(1)/(3))^(2)+12(y-1)^(2)=1`

B

`12(x-(1)/(3))^(2)+9(y-1)^(2)=1`

C

`(x-(1)/(2))^(2)+((y-2)^(2))/(9)=1`

D

`3(x+(1)/(2))^(2)+4(y-1)^(2)=1`

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A
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Knowledge Check

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

    A
    `3x^2 + 4y^2 = 1`
    B
    `3x^2 + 4y^2 = 12`
    C
    `4x^2 + 3y^2 = 12`
    D
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    A
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    B
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    C
    `5 sqrt(2)`
    D
    none of these

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