Consider two straight lines, each of which is tangent to both the circle x² + y² = 1/2 and the parabola y² = 4x. Let these lines intersect at the point Q. Consider the ellipse whose center is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is √2, then which of the following statement(s) is (are) TRUE?