1.1. The expression ${x}^{2}—8x+21$ can be written in the form ${(x-a)}^{2}+b$ for all values of $x$.

Find the value of $a$ and the value of $b$.

1.2. The equation of a curve is $y=f(x)$ where $f(x)={x}^{2}—8x+21$

The diagram shows part of a sketch of the graph of $y=f(x)$.

The minimum point of the curve is $M$.

Write down the coordinates of $M$.