The centres of those circles which touch the circle, $x^2+y^2- 8x -8y-4 = 0,$ externally and also touch the x-axis, lie on:

Question

$\begin{array}{1 1} \text{(1) a circle}\\ \text{(2) an ellipse which is not a circle} \\ \text{(3) a hyperbola} \\ \text{(4) a parabola}\end{array}$