Consider a line \(L:3x+4y-10=0\).
Consider a circle \(S_1:x^2+y^2-16x-18y+109=0\).
Find the equation of a certain circle \(S_2\) which satisfies the 3 conditions below:
\(S_2\) touches \(S_1\) externally.
\(S_2\) touches \(L\).
Line joining the centers of \(S_1\) and \(S_2\) is perpendicular to \(L\).
Do post nice solutions and hints!