A circle \(C _ { 1 }\) has equation
$$x ^ { 2 } + y ^ { 2 } + 18 x - 2 y + 30 = 0$$
The line \(l\) is the tangent to \(C _ { 1 }\) at the point \(P ( - 5,7 )\).
Find an equation of \(l\) in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found.
A different circle \(C _ { 2 }\) has equation
$$x ^ { 2 } + y ^ { 2 } - 8 x + 12 y + k = 0$$
where \(k\) is a constant.
Given that \(C _ { 2 }\) lies entirely in the 4th quadrant, find the range of possible values for \(k\). [0pt]
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