Adding graphics showing $\pm\Delta_{c^1}$, $\pm\Delta_{c^2}$, $\pm\Delta_{c^3}$ to a plot

I have a ellipsoid equation given bellow. I want to find $$\pm\Delta_{c^1}$$, $$\pm\Delta_{c^2}$$, $$\pm\Delta_{c^3}$$ around the point $$(81.32, 10.62, 17.17)$$

Show[
ContourPlot3D[
425182.22 + 64.14985 c1^2 + 2.176 c2^2 +
c2 (-1.013*10^-13 - 0.006 c3) +
c1 (-10442.15 - 0.567c2 + 0.863846077 c3) -
70.3549202 c3 + 0.0052366 c3^2 == 1,
{c1,81,81.7}, {c2,9,12},{c3,-5,40},
AxesLabel -> {c1, c2, c3},
ContourStyle -> Directive[Orange, Opacity[0.7]],
LabelStyle -> Directive[Black, 15],
Mesh-> None],
Graphics3D[{Black, PointSize[0.015], Point[{81.32, 10.62, 17.17}]}]]
• The meaning of $\pm\Delta_{c^1}$, $\pm\Delta_{c^2}$, $\pm\Delta_{c^3}$ may be clear to you, but not to me. Definitions for these quantities are needed. – m_goldberg Jan 20 at 13:40
• Sorry. Just leave that part. I asked something wrong. Leave that part. I only need the projection. – Sahabub Jahedi Jan 20 at 15:58

f = 425182.22 + 64.14985 c1^2 + 2.176 c2^2 +
c2 (-1.013*10^-13 - 0.006 c3) +
c1 (-10442.15 - 0.567 c2 + 0.863846077 c3) - 70.3549202 c3 +
0.0052366 c3^2 - 1;

c = {c1, c2, c3};
(*Finding the center by finding the minimum of the quadratic function*)

center = c /. Solve[D[f, {c, 1}] == {0, 0, 0}, c][[1]];
x = {x1, x2, x3};
(*Finding the principal axes with  Eigensystem.*)
A = 1/2 D[f /. Thread[c -> x], {x, 2}] /(-f /. Thread[c -> center]);
{a, e} = Eigensystem[A];
paxes = 1/Sqrt[a] e;

contour =
ContourPlot3D[f == 0, {c1, 81, 81.7}, {c2, 9, 12}, {c3, -5, 40},
PlotPoints -> 60,
ContourStyle -> Opacity[.25],
Mesh -> None
];

Show[
contour,
Graphics3D[{Opacity[0.25], Blue,
Ellipsoid[center, Inverse[A]], PointSize[Large],
Point[center],
Thick, Black, Opacity[1],
Red, Line[{center, center + paxes[[1]]}],
Green, Line[{center, center + paxes[[2]]}],
Blue, Line[{center, center + paxes[[3]]}]
}]
]
• Thank you so much. – Sahabub Jahedi Jan 20 at 15:58
• You're welcome. – Henrik Schumacher Jan 20 at 17:14