The figure that you have drawn should show that the common tangent to the circle and the hyperbola is the vertical line x=1. That tells you that the ellipse has its centre on the x-axis, and its major axis parallel to the x-axis. Say that the centre is at the point (c,1). If the eccentricity is e, the major semi-axis has length a and the minor semi-axis has length b, then you should know that the distance from the centre to the focus is ae, the distance from the centre to the directrix is a/e, and b is given by . Use those facts to find a, b and c. Then the equation of the ellipse is