An ellipse has eccentricity $\frac{1}{2}$ and one focus at the point $P\left( {\frac{1}{2},\;1} \right)$. Its one directrix is the common tangent nearer to the point $P$, to the circle ${x^2} + {y^2} = 1$ and the hyperbola ${x^2} - {y^2} = 1$. The equation of the ellipse in the standard form, is
An ellipse has eccentricity $\frac{1}{2}$ and one focus at the point $P\left( {\frac{1}{2},\;1} \right)$. Its one directrix is the common tangent nearer to the point $P$, to the circle ${x^2} + {y^2} = 1$ and the hyperbola ${x^2} - {y^2} = 1$. The equation of the ellipse in the standard form, is
- [IIT 1996]
- A
$\frac{{{{(x - 1/3)}^2}}}{{1/9}} + \frac{{{{(y - 1)}^2}}}{{1/12}} = 1$
- B
$\frac{{{{(x - 1/3)}^2}}}{{1/9}} + \frac{{{{(y + 1)}^2}}}{{1/12}} = 1$
- C
$\frac{{{{(x - 1/3)}^2}}}{{1/9}} - \frac{{{{(y - 1)}^2}}}{{1/12}} = 1$
- D
$\frac{{{{(x - 1/3)}^2}}}{{1/9}} - \frac{{{{(y + 1)}^2}}}{{1/12}} = 1$
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