This problem involves finding the angle between common tangents of an ellipse and a circle, specifically with respect to the minor axis of the ellipse. We will use the conditions for a line to be tangent to an ellipse and a circle, and then determine the orientation of the minor axis to calculate the required angle.

1. Understand the Standard Forms and Tangency Conditions

• Standard Ellipse Equation: An ellipse centered at the origin is given by $\frac{x^2}{A^2} + \frac{y^2}{B^2} = 1$.
  • If $A^2 > B^2$, the major axis is along the x-axis (length $2A$), and the minor axis is along the y-axis (length $