Let the straight line \( y = 2x \) touch a circle with centre \( (0, \alpha) \), \( \alpha > 0 \), and radius \( r \) at a point \( A_1 \). Let \( B_1 \) be the point on the circle such that the line segment \( A_1B_1 \) is a diameter of the circle. Let \( \alpha + r = 5 + \sqrt{5} \).
Match each entry in List-I to the correct entry in List-II.
The correct option is:
