So here is my first attempt at posting a reply to any question. Help me if i go wrong
To figure out whether these two intersect, we can solve their equations.
Equating the RHS of both equations, we get :
\(ax - b = x^2 + b\)
\(x^2 - ax + 2b = 0\)
This is of the form\(A x^2 + B x + C = 0\)
So if the equation has real numbers as roots, we can conclude that the parabola and circle do intersect.
For the equation to have real roots, \(B^2 - 4AC\) should be a positive number, so that \(\sqrt{B^2-4AC}\) is real.
In our equation \(B^2 - 4AC = a^2 - 4*1*2b = a^2 - 8b\)
We don't know whether \(a^2> 8b\) from (1). Therefore we don't know if the equation has real roots.
From (2), we can conclude that since b<0 , -8b>0. Therefore, \(B^2-4AC\) is positive. Hence, the answer should be B.
Therefore, in my opinion the answer should be E.