My bad. Jumped on "5" and got nice integer solutions: k=1 or k=3;
both "looked" good on my quickly sketched diagram
BUT: if the correct "25" is used, then : k = [6 +- sqrt(-6)] / 3;
so no real solution.
Perhaps the OP made a typo....
I suspect that whoever wrote the question made the mistake.
The 5 does give a very nice solution. So it should have been .