<< "Graphics`ImplicitPlot`"

\(Do[g1\  = 
        ImplicitPlot[

          			{x\^2 - y\^2 == 4, \((x - 4)\)\^2 - y\^2 == 3, 
            \((x - \(4\ k\)\/\(1 + k\))\)\^2 - y\^2 == 
              \(3\ k\^2 - 9\ k + 4\)\/\((1 + k)\)\^2}, 

          	{x, \(-3\), 7}, {y, \(-4\), 4}, 
	
          PlotStyle -> {RGBColor[0, 0, 0], RGBColor[0, 0, 0], 
              RGBColor[1, 0, 0]}, 
	AxesLabel -> {"x", "y`"}, 

          			DisplayFunction -> Identity
	]; 
	
      g2\  = ImplicitPlot[
          
{x\^2 + y\^2 == 4, \((x - 4)\)\^2 + y\^2 == 3, 
            \((x - \(4\ k\)\/\(1 + k\))\)\^2 + y\^2 == 
              \(3\ k\^2 - 9\ k + 4\)\/\((1 + k)\)\^2}, 

          			{x, \(-3\), 7}, {y, \(-4\), 4}, 
			
          PlotStyle -> {RGBColor[0, 0, 0], RGBColor[0, 0, 0], 
              RGBColor[1, 0, 0]}, 
			AxesLabel -> {"x", "y"}, 

          			DisplayFunction -> Identity
			]; 
	
      \(Show[GraphicsArray[{g1, g2}]]; \)			

      	, {k, \(-0.45\), 3.95, 0.1}]\)