Solving the System: x^2+(y-5)^2=9 and y=x^2+K

[answerseeker]

Q: If K>0, for what values of k does the system x^2+ (y-5)^2=9 and y=x^2 +K have:

a) 4 solutions
b) no solution

i have no idea how to begin this problem. I know that centre of circle is 5,0 and radius is 3 and the second eqn is a parabola..but that's about it so far..
any ideas?

 

[Tide]

The center of the circle is (0, 5). I recommend making a sketch of the graphs and I think you'll find it quite illuminating! :)