A line has equation $y = kx + 6$ and a curve has equation $y = {x^2} + 3x + 2k$, where $k$ is a constant.
a) For the case where $k = 2$, the line and the curve intersect at points $A$ and $B$. Find the distance $AB$ and the coordinates of the mid-point of $AB$.
b) Find the two values of $k$ for which the line is a tangent to the curve.
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