Looping with "Table" abreast over more than two variables

Question

Clear["Global`*"]
S1 = Inverse[{{0.5, 0}, {0, 0.2}}];
R1 = RotationMatrix[Pi/3];
p1 = {1, 1};

S2 = Inverse[{{1, 0}, {0, 0.5}}];
R2 = RotationMatrix[Pi/6];
p2 = {2, 2};

H1 = R1 . Transpose[S1] . S1 . Transpose[R1];
J1 = -(H1 . p1 + Transpose[H1] . p1);
C1 = p1 . H1 . p1 - 1;

H2 = R2 . Transpose[S2] . S2 . Transpose[R2];
J2 = -(H2 . p2 + Transpose[H2] . p2);
C2 = p2 . H2 . p2 - 1;

Show[Table[Graphics[{Red, Point[p]}], {p, {p1, p2}}],
 Table[ContourPlot[{x, y} . H . {x, y} + Transpose[J] . {x, y} + C == 
    0, {x, -5, 5}, {y, -5, 5}], {H, {H1, H2}}, {J, {J1, J2}}, {C, {C1,
     C2}}], Axes -> True, AxesOrigin -> {0，0}]

which gives me the eight ellipses because of Descarte product on three variables each which takes two values.

What I want is by using Table to generate an output where value of H , J and C start at the same time such as to get {{first value of H,first value of J,first value of C},{second value of H,second value of J,second value of C},{third value of H,third value of J,third value of C}}. In the example above, the output would be two ellipse.

There is one similar question which provides two methods.

One is adding Diagonal, but here is three variables not two variables. Diagonal would gives three results.

The other is using MapThread instead of Table, but ContourPlot is not a math function.

Thank you for any and all suggestions

Answer 1

In addition to what you have:

H = {H1, H2};
J = {J1, J2};
Cx = {C1, C2};
exprs = Table[{x, y} . H[[i]] . {x, y} + Transpose[J[[i]]] . {x, y} + 
   Cx[[i]], {i, 1, 2}]

{9.81347 - 21.3135 x + x (19.75 x - 9.09327 y) - 0.313467 y + 
  y (-9.09327 x + 9.25 y), 
 8.6077 - 1.80385 x + x (1.75 x - 1.29904 y) - 7.80385 y + 
  y (-1.29904 x + 3.25 y)}

Show[
 ContourPlot[exprs, {x, 0, 3}, {y, 0, 3}
  , Axes -> True
  , AxesOrigin -> {0，0}
  , Epilog -> {Red, AbsolutePointSize[5],
    Point@{p1, p2}}
  ]
 ]