M$/$J $19/$P$12/$Q$9$

The curve $C_1$ has equation $y=x^2-4x+7.$ The curve $C_2$ has 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

$[2]$ value of $k$ and the coordinates of $P.$

$[8$