Problem 1
Part of 1995 VJIMC
Problems(2)
solvability of system
Source: VJIMC 1995 1.1
10/27/2021
Discuss the solvability of the equations
\begin{align*}\lambda x+y+z&=a\\x+\lambda y+z&=b\\x+y+\lambda z&=c\end{align*}for all numbers .
algebralinear algebra
hyperbolas orthogonal?
Source: VJIMC 1995 2.1
11/15/2021
Prove that the systems of hyperbolas
\begin{align*}x^2-y^2&=a\\xy&=b\end{align*}are orthogonal.
conicshyperbola