MathDB

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}=p/q

, where

p

and

q

are relatively prime integers, find

p+q

Problem Statement