Question 37
The graph of the hyperbola $y = \frac{1}{x}$ is drawn on the Cartesian plane $Oxy$. Three snails start simultaneously from the origin $O$ and move along the abscissa axis $Ox$ (each snail has its constant speed). Let $A(t)$, $B(t)$ and $C(t)$ be points on the graph of the hyperbola such that their abscissae are equal to the abscissae of the first, the second and the third snails at the moment $t$, respectively.
Prove that the area of the triangle $ABC$ is independent of time.
Prove that the area of the triangle $ABC$ is independent of time.