在平面直角坐标系\(xOy\)中，已知圆\(C_{1}\)：\(x^{2}+y^{2}=16\)和圆\(C_{2}\)：\((x-7)^{2}+(y-4)^{2}=4.\)

\((1)\)求过点\((4,6)\)的圆\(C_{1}\)的切线方程；

\((2)\)设\(P\)为坐标平面上的点，且满足：存在过点\(P\)的无穷多对互相垂直的直线\(l_{1}\)和\(l_{2}\)，它们分别与圆\(C_{1}\)和圆\(C_{2}\)相交，且直线\(l_{1}\)被圆\(C_{1}\)截得的弦长是直线\(l_{2}\)被圆\(C_{2}\)截得的弦长的\(2\)倍．试求所有满足条件的点\(P\)的坐标．