Find the values of k for which the line y=( 1/2) x + k is a tangent to the curve x^2+y^2=8k

I tried equating the two equations together, making a new combined equation.

from that equation, I took out it's b^2 -4ac and equated it to 0. Haha I hope you can understand what I just wrote.

Anyway If not how should I do this question? Thank you very much!!