An ellipse has eccentricity \( 1 / 2 \) and one focus at the point \( P\left(\frac{1}{2}, 1\righ...

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An ellipse has eccentricity \( 1 / 2 \) 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
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