{a=1/2;
b=1/Sqrt[2];ContourPlot[(x^2+y^2+2a x)^2==4a^2(x^2+y^2),{x,-2,2},{y,-2,2}],
ContourPlot[(x^2+y^2+2a x)^2==4b^2(x^2+y^2),{x,-3,1},{y,-2,2}],a=1;
ContourPlot[(a x^2+a y^2+x)^2==(x^2+y^2)+y/a ,{x,-3,1},{y,-2,2}],
ContourPlot[(12a x^2+10a y^2+10x)^2==130 x^2+100y^2,{x,-3,1},{y,-2,2}]}