If the circle `C_1: x^2 + y^2 = 16` intersects another circle `C_2` of radius `5` in such a manner that,the common chord is of maximum length and has a slope equal to `3/4`, then the co-ordinates of the centre of `C_2` are:
A. (-9/5, 12/5), (9/5, -12/5)
B. (-9/5, -12/5), (9/5, 12/5)
C. (12/5, -9/5), (-12/5, 9/5)
D. none of these
