The graph of the parametric equations

Question

x=cos(t)
y=sin(t)
meets the graph of the parametric equations
x=2+4cos(s)
y=3+4sin(s)
at two points. Find the slope of the line between these two points.

So far I've set up the system of equations
cos(t)=2+4cos(s)
sin(t)=3+4sin(s)
but it seems to be getting me nowhere.

Answer 1

since sin^2(t)+cos^2(t) = 1,

(2+4cos(s))^2 + (3+4sin(s))^2 = 1

See where that gets you.