- The curve \(C _ { 1 }\) has equation
$$y = x ^ { 2 } + k x - 9$$
and the curve \(C _ { 2 }\) has equation
$$y = - 3 x ^ { 2 } - 5 x + k$$
where \(k\) is a constant.
Given that \(C _ { 1 }\) and \(C _ { 2 }\) meet at a single point \(P\)
- show that
$$k ^ { 2 } + 26 k + 169 = 0$$
- Hence find the coordinates of \(P\)