Find all values of the parameter $k$ for which the system of inequalities \begin{align*} ky^2+4ky-2x+6k+3&\le0\\ kx^2-2y-2kx+3k-3&\le0 \end{align*}has a unique solution.
Source: Ukraine 1999 Grade 11 P2
Tags: inequalities
Find all values of the parameter $k$ for which the system of inequalities \begin{align*} ky^2+4ky-2x+6k+3&\le0\\ kx^2-2y-2kx+3k-3&\le0 \end{align*}has a unique solution.