Question 77
Given two hyperbolae $H_1$ and $H_2$ with the equations $y = 1/x$ and $y = -1/x$, respectively. A straight line meets $H_1$ at points $A$ and $B$, and meets $H_2$ at points $C$ and $D$. The lines tangent to $H_1$ at points $A$ and $B$ intersect at point $M$, and the lines tangent to $H_2$ at points $C$ and $D$ intersect at point $N$.
Prove that $M$ and $N$ are symmetric with respect to the origin of coordinates.
Prove that $M$ and $N$ are symmetric with respect to the origin of coordinates.