a) A straight line passes through the point $\left( {2,{\text{ }}0} \right)$ and has gradient $m$. Write down the equation of the line.
b) Find the two values of $m$ for which the line is a tangent to the curve $y = {x^2} - 4x + 5$. For each value of $m$, find the coordinates of the point where the line touches the curve.
c) Express ${x^2} - 4x + 5$ in the form ${\left( {x + \alpha } \right)^2} + b$ and hence, or otherwise, write down the coordinates of the minimum point on the curve.
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