Question 22
A parabola $y = a x^2$, $a \gt 0$, and the hyperbola $y = 1/x$ meet at point $T$. The common tangent of these curves touches the hyperbola at point $Q$ and touches the parabola at point $P$.
a) Prove that some two medians of the triangle $PQT$ are perpendicular.
b) Determine the area of the triangle $PQT$.
(V. Karamzin)
a) Prove that some two medians of the triangle $PQT$ are perpendicular.
b) Determine the area of the triangle $PQT$.
(V. Karamzin)