A[x_]:=-1 +(x+1) HeavisidePi[x/2] + 2HeavisideTheta[x-1]

B[x_]:=Sqrt[1-A[x-2]^2]+Sqrt[1-A[x+2]^2]

T[x_,s_]:=Sqrt[(16(1-s)+9s)-x^2]

H[s_,x_]:=s B[x]+(1-s) T[x,s]

Plot[{H[0,x],-H[0,x],H[1,x],-H[1,x]},{x,-4,4},PlotStyle->{Green,Green,Red,Red},AspectRatio->1]

Plot[{H[0,x],H[.2,x],H[.4,x],H[.6,x],H[.8,x],H[1,x]},{x,-4,4}]

Animate[Plot[{H[0,x],-H[0,x],H[s,x],-H[s,x],H[1,x],-H[1,x]},{x,-4,4},PlotStyle->{Black,Black,Green,Green,Red,Red},AspectRatio->1],{s,0,1},AnimationRunning->False]