4．The line with equation \(y = m x\) is a tangent to the circle \(C _ { 1 }\) with equation $$( x + 4 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 13$$ （a）Show that \(m\) satisfies the equation $$3 m ^ { 2 } + 56 m + 36 = 0$$ The tangents from the origin \(O\) to \(C _ { 1 }\) touch \(C _ { 1 }\) at the points \(A\) and \(B\) ．
（b）Find the coordinates of the points \(A\) and \(B\) ．
（8）
Another circle \(C _ { 2 }\) has equation \(x ^ { 2 } + y ^ { 2 } = 13\) ．The tangents from the point \(( 4 , - 7 )\) to \(C _ { 2 }\) touch it at the points \(P\) and \(Q\) ．
（c）Find the coordinates of either the point \(P\) or the point \(Q\) ．
（2）