Question: Maredn"s theorem

restart;
with(geometry);
with(plots);
_EnvHorizontalName = 'x';
_EnvVerticalName = 'y';
point(A, -3, 9);
point(B, -5, 0);
point(C, 6, 0);
xA := -3;
yA := 9;
xB := -5;
yB := 0;
xC := 6;
yC := 0;
triangle(ABC, [A, B, C]);
midpoint(M2, A, C);
midpoint(M1, B, C);
midpoint(M3, A, B);
coordinates(M1);
coordinates(M2);
coordinates(M3);
segment(sA, [A, M1]);
segment(sB, [B, M2]);
segment(sC, [C, M3]);
centroid(G, ABC);
midpoint(J1, A, G);
midpoint(J2, B, G);
midpoint(J3, C, G);
coordinates(J1);
coordinates(J2);
coordinates(J3);
zA := xA + yA*I;
zB := xB + yB*I;
zC := xC + yC*I:
diff((z - zA)*(z - zB)*(z - zC), z)*I;);
allvalues(%, z)
;I am trying to find focus of Steiner ellipse with Marden's theoreme. Thank you.