An ellipse has eccentricity 12 and one of the foci at the point S(12,1). One of the directrices of the ellipse is the common tangent to the circle x2+y2=1 and the hyperbola x2−y2=1, corresponding to the focus S. The equation of the ellipse in standard form is

An ellipse has eccentricity 12 and one of the foci at the point S(12,1

1.	An ellipse has eccentricity 12 and one of the foci at the point S(12,1). One of the directrices of the ellipse is the common tangent to the circle x2+y2=1 and the hyperbola x2−y2=1, corresponding to the focus S. The equation of the ellipse in standard form is
Answer» An ellipse has eccentricity $\frac{1}{2}$ and one of the foci at the point $S (\frac{1}{2}, 1) .$ One of the directrices of the ellipse is the common tangent to the circle $x^{2} + y^{2} = 1$ and the hyperbola $x^{2} - y^{2} = 1,$ corresponding to the focus $S .$ The equation of the ellipse in standard form is