$\Delta \cap Ox=M(m;0)$
$\Delta \cap Oy=N(0;n)$
(với $m, n\ne 0$)
$\to \Delta: \dfrac{x}{m}+\dfrac{y}{n}=1$
$A(2;3)\in \Delta\to \dfrac{2}{m}+\dfrac{3}{n}=1$
$\to 2n+3m=mn$
$S_{OMN}=\dfrac{1}{2}|mn|=2$
$\to |mn|=4$
- Nếu $mn=4$:
$\to 2n+3m=4$
$\to n=\dfrac{4-3m}{2}$
$\to \dfrac{m(4-3m)}{2}=4$
$\to -3m^2+4m-8=0$ (vô nghiệm, loại)
- Nếu $mn=-4$:
$\to 2n+3m=-4$
$\to n=\dfrac{-3m-4}{2}$
$\to \dfrac{m(-3m-4)}{2}=-4$
$\to -3m^2-4m+8=0$
$\to m=\dfrac{-2\pm2\sqrt7}{3}$
$m=\dfrac{-2-2\sqrt7}{3}\to n=\sqrt7-1$
$m=\dfrac{-2+2\sqrt7}{3}\to n=-\sqrt7-1$
Vậy $\Delta: \dfrac{3x}{-2-2\sqrt7}+\dfrac{y}{\sqrt7-1}=1$ hoặc $\Delta: \dfrac{3x}{-2+2\sqrt7}+\dfrac{y}{-\sqrt7-1}=1$
