Shortest pipe from a tank to a straight road

On a map with units in kilometres, a straight road has equation \(3x+4y=12\) and meets a highway (the \(y\)-axis) at \(J(0,3)\). A water tank stands at \(P(6,7)\). A straight pipe is to be laid from \(P\) to a junction point \(F\) on the road, and the pipe costs \(\$40\,000\) per km. Assume the land between \(P\) and the road allows a straight pipe.

1. Given that the pipe is to be as short as possible, find the coordinates of \(F\).[4]
2. Find the length of the pipe and its cost.[2]
3. The council then requires the junction to be at least \(3\) km from \(J\). Explain why \(F\) is no longer allowed, and find the coordinates of the allowed junction point that gives the shortest pipe.[3]