Primka[a_, c_]:=Cos[a]*x+Sin[a]*y-c

Manipulate[Grid[{{Show[ContourPlot[Primka[a,c]==0,{x,-11, 11}, {y,-11, 11}, ContourStyle->{Red, Thickness[0.01]}], FrameLabel->{"x","y"}, ImageSize->{300, 300}], Show[Graphics[{PointSize[0.03], Red, Point[{a,c}]}], PlotRange->{{-Pi, Pi}, {0,10}}, Frame->True, FrameLabel->{"α","c"}, ImageSize->{300, 300}]}}],{{a,0},-Pi,Pi}, {{c, 0},0,10}]

cc={x->5*t, y->0}

acPoints={}
na=50
nc=50

For[i=0,i<(na+1),i++,
	For[j=0,j<(nc+1),j++,
		tmpC=i*10/nc;
		tmpA=-Pi+2*Pi*j/na;
		tmp=CountRoots[N[Primka[tmpA,tmpC]/.cc], {t,0,1}];
		If[tmp>0, AppendTo[acPoints, {tmpA, tmpC}]]
			
]]

pc=Graphics[{PointSize[0.03], Blue,  Point[acPoints]}];

Manipulate[Grid[{{Show[ContourPlot[Primka[a,c]==0,{x,-11, 11}, {y,-11, 11}, ContourStyle->{Red, Thickness[0.01]}], ParametricPlot[{x,y}/.cc, {t,0,1}, PlotStyle->{Blue, Thickness[0.01]}], FrameLabel->{"x","y"}, ImageSize->{300, 300}], Show[pc,Graphics[{PointSize[0.03], Red, Point[{a,c}]}], PlotRange->{{-Pi, Pi}, {0,10}}, Frame->True, FrameLabel->{"α","c"}, ImageSize->{300, 300}]}}],{{a,0},-Pi,Pi}, {{c, 0},0,10}]

cc1={x->5*t+2, y->0}

acPoints={}
na=20
nc=20

For[i=0,i<(na+1),i++,
	For[j=0,j<(nc+1),j++,
		tmpC=i*10/nc;
		tmpA=-Pi+2*Pi*j/na;
		tmp=CountRoots[N[Primka[tmpA,tmpC]/.cc1], {t,0,1}];
		If[tmp>0, AppendTo[acPoints, {tmpA, tmpC}]]
			
]]

pc1=Graphics[{PointSize[0.03], Blue,  Point[acPoints]}];

Manipulate[Grid[{{Show[ContourPlot[Primka[a,c]==0,{x,-11, 11}, {y,-11, 11}, ContourStyle->{Red, Thickness[0.01]}], ParametricPlot[{x,y}/.cc1, {t,0,1}, PlotStyle->{Blue, Thickness[0.01]}], FrameLabel->{"x","y"}, ImageSize->{300, 300}], Show[pc1,Graphics[{PointSize[0.03], Red, Point[{a,c}]}], PlotRange->{{-Pi, Pi}, {0,10}}, Frame->True, FrameLabel->{"α","c"}, ImageSize->{300, 300}]}}],{{a,0},-Pi,Pi}, {{c, 0},0,10}]