The curve \(C_1\) has the equation \(y = x^2 - 4x + 7\). The curve \(C_2\) has the equation \(y^2 = 4x + k\), where \(k\) is a constant. The tangent to \(C_1\) at the point where \(x = 3\) is also the tangent to \(C_2\) at the point \(P\). Find the value of \(k\) and the coordinates of \(P\).