8. Given that
$$x ^ { 2 } + 10 x + 36 = ( x + a ) ^ { 2 } + b$$
where \(a\) and \(b\) are constants,
- find the value of \(a\) and the value of \(b\).
- Hence show that the equation \(x ^ { 2 } + 10 x + 36 = 0\) has no real roots.
The equation \(x ^ { 2 } + 10 x + k = 0\) has equal roots.
- Find the value of \(k\).
- For this value of \(k\), sketch the graph of \(y = x ^ { 2 } + 10 x + k\), showing the coordinates of any points at which the graph meets the coordinate axes.