The circle in the diagram has equation $(x - 4)^2 + (y + 1)^2 = 40$. Two parallel tangents, both having gradient $1$, meet the circle at $A$ and $B$.
(a)[3]
Determine the equation of line $AB$, and present your answer in the form $y = mx + c$.
(b)[4]
Determine the coordinates of $A$, with both coordinates expressed in surd form.
(c)[2]
Determine the equation of the tangent at $A$, with your answer in the form $y = mx + c$ and $c$ written in surd form.
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