L & # 39; writing:

```
{c1, c2, c3, c4, c5} = N({Tan(E), Sin(E), Tanh(E), E, Sinh(E)});
a = (c1 + c3) / 2;
b = Sqrt(c5^2 - (c2 - c4)^2) / 2;
c = 0;
d = (c2 + c4) / 2;
e = (c1 - c3) (c2 - c4) / (4 b);
f = c5 Sqrt(c5^2 - (c1 - c3)^2 - (c2 - c4)^2) / (4 b);
x = a + b Cos(t) + c Sin(t);
y = d + e Cos(t) + f Sin(t);
xmin = Minimize({x, 0 <= t <= 2π}, t)((1));
xmax = Maximize({x, 0 <= t <= 2π}, t)((1));
FullSimplify((xmin + xmax) / 2 == a)
ymin = Minimize({y, 0 <= t <= 2π}, t)((1));
ymax = Maximize({y, 0 <= t <= 2π}, t)((1));
FullSimplify((ymin + ymax) / 2 == d)
```

we have:

True

True

this is what is desired. However, by making a simple change:

```
{c1, c2, c3, c4, c5} = {Tan(E), Sin(E), Tanh(E), E, Sinh(E)};
```

we have:

True

...

that is to say, in the second case, there is no answer. So by defining the constants this other way:

```
SetAttributes(c1, Constant)
NumericQ(c1) = True;
N(c1, prec___) := N(Tan(E), prec)
SetAttributes(c2, Constant)
NumericQ(c2) = True;
N(c2, prec___) := N(Sin(E), prec)
SetAttributes(c3, Constant)
NumericQ(c3) = True;
N(c3, prec___) := N(Tanh(E), prec)
SetAttributes(c4, Constant)
NumericQ(c4) = True;
N(c4, prec___) := N(E, prec)
SetAttributes(c5, Constant)
NumericQ(c5) = True;
N(c5, prec___) := N(Sinh(E), prec)
```

we have:

True

Minimize :: infeas: There are no values of {t} for which the constraints 0 <= t <= 2π are satisfied and the objective function (...) has a real value.

Maximize :: infeas: There are no values of {t} for which the constraints 0 <= t <= 2π are satisfied and the objective function (...) has a real value.

Infinity :: indet: Indeterminate expression -∞ + ∞ encountered.

Undetermined == (c2 + c4) / 2

where, apparently, another problem arises. How to solve everything?