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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

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

B

`((x-(1)/(3))^(2))/((1)/(8))+((y-1)^(2))/((1)/(12))=1`

C

`((x-(1)/(3))^(2))/((1)/(9))+((y-1)^(2))/((1)/(8))=1`

D

None of these

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The correct Answer is:
A
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