A geometry problem by Soumava Pal

It is a well known fact that the triangle with vertices with coordinates $(a,\frac{c}{a})$ , $(b,\frac{c}{b})$ , $(d,\frac{c}{d})$ , that is with the vertices lying on a hyperbola, a rectangular hyperbola $xy=c=1$ in this case, the orthocenter of the triangle also lies on the hyperbola $xy=c$ and is given by $(\frac{-1}{abd},-cabd)$ , and the hyperbola is also known as the Jerabek Hyperbola .