2005 AIME II Problem 15

Let w_1 and w_2 denote the circles x^2+y^2+10x-24y-87=0 and x^2 +y^2-10x-24y+153=0, respectively. Let m be the smallest positive value of a for which the line y=ax contains the center of a circle that is externally tangent to w_2 and internally tangent to w_1. Given that m^2=\frac pq, where p and q are relatively prime integers, find p+q.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.