Saddels, cases Δ < 0, τ = 0

How do saddles look and behave in the case of  Δ < 0, τ = 0, i.e., on the negative part of the horizontal axis of the Δτ-classification graph for linear homogenous 2-D systems.

Condition for restricting coefficients a, b, c, d for cases Δ < 0, τ = 0

Clear[a,b,c,d]
A=(({{a, b}, {c, d}}));
Det[A]<0
Tr[A]==0

Phase portrait rendering

Manipulate[
Module[{a,d,A,ev},

d=-aa;
A={{aa,bb},{cc,d}};
ev=Eigenvectors[A];

Column[{
Style[
If[-(aa^2)<bb*cc,"SADDLE","Not a SADDLE"],(*Condition for saddles*)
Bold,20
],
MatrixForm[A],
"Determinant: "<>ToString[Det[A]],
"Trace: "<>ToString[Tr[A]],

Show[
StreamDensityPlot[A.{x,y},{x,-2,2},{y,-2,2},
FrameLabel->{"x(t)","y(t)"},
LabelStyle->14,
ImageSize->500,
ColorFunction->"LakeColors"],

Graphics[{Thick,Red,Arrow[{{0,0},Normalize[#]}]&/@ev}],Graphics[{PointSize[Large],Red,Point[{0,0}]}]
]
}, Center]
],

{{aa,1,"coefficient a"},-10,10,Appearance->"Labeled"},
{{bb,0,"coefficient b"},-20,20,Appearance->"Labeled"},{{cc,0,"coefficient c"},-20,20,Appearance->"Labeled"},

SaveDefinitions->True,
TrackedSymbols:>{aa, bb,cc}]