Question 83
Given two hyperbolae $H_1$ and $H_2$ with the equations $y = 1/x$ and $y = -1/x$, respectively. Let $M$ be an arbitrary point on $H_1$. Let $M_1$ and $M_2$ be the tangency points of the lines $MM_1$ and $MM_2$ with the hyperbola $H_2$.
Prove that the line $M_1M_2$ is tangent line of $H_1$.
Prove that the line $M_1M_2$ is tangent line of $H_1$.