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Find the equation of the center of the Kiepert hyperbola: a) in trilinear coordinates; b) in barycentric coordinates.

#
The Kiepert hyperbola equation was obtained in the solution of problem 31.081. Therefore, using problem $\underline{31.077}$, we get that the barycentric coordinates of the center of the Kiepert hyperbola are

$$
\left(\left(b^{2}-c^{2}\right)^{2}:\left(c^{2}-a^{2}\right)^{2}:\left(a^{2}-b^{2}\right)^{2}\right)
$$

Accordingly, its trilinear coordinates are

$$
\left(\frac{\left(b^{2}-c^{2}\right)^{2}}{2}: \frac{\left(c^{2}-a^{2}\right)^{2}}{2}: \frac{\left(a^{2}-b^{2}\right)^{2}}{2}\right)
$$

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