The circles C₁ : x² + y² = 9 and C₂ : (x − 3)² + (y − 4)² = 16 intersect at X and Y. Another circle C₃ : (x − h)² + (y − k)² = r² has its centre collinear with the centres of C₁ and C₂; C₁ and C₂ lie inside C₃; and C₃ touches C₁ at M and C₂ at N. The line through X and Y intersects C₃ at Z and W, and a common tangent of C₁ and C₃ is tangent to x² = 8αy. List-I: (I) 2h + k; (II) length ZW/length XY; (III) area of triangle MZN/area of triangle ZMW; (IV) α. List-II: (P) 6; (Q) √6; (R) 5/4; (S) 21/5; (T) 2√6; (U) 10/3.
Which of the following is the only CORRECT combination?