10.1. Plot on the coordinate plane the set of points whose coordinates satisfy the equation $\left(x^{2}+3 x y+2 y^{2}\right)\left(x^{2} y^{2}-1\right)=0$.
Solution. Factoring the first bracket into $(x+2 y)(x+y)$, and the second into $(x y+1)(x y-1)$, we obtain that the desired set is the union of two lines $y=-x, y=-x / 2$ and two hyperbolas $y=1 / x, y=-1 / x$.