Find the sum of all possible values of the constant such that the graph of the parametric equations

intersects the graph of the parametric equations

at only one point.

I tried using sin^2+cos^2=1 again, ending up with

x^2 = 4 + 16 cos^2(s) + 16 cos(s)

y^2 = k^2 + 16 sin^2(s) - 8k sin(s)

Thus

x^2 + y^2 = 16(1) + 4 + k^2 + 16 cos(s) - 8k sin(s)

From here I wondered if I should substitute in sin(s)= (k-y)/4 but would that just take me in circles?

Thank you