Thay $y=0$ vào $d$:
$mx-2m-1=0\Leftrightarrow x=\dfrac{2m+1}{m}$
$\Rightarrow A\Big(\dfrac{2m+1}{m};0\Big)$
Thay $x=0$ vào $d$:
$0m-2m-1=y\Leftrightarrow y=-2m-1$
$\Rightarrow B(0;-2m-1)$
$S_{OAB}=\dfrac{1}{2}OA.OB=\dfrac{1}{2}\Big| \dfrac{2m+1}{m}.(-2m-1)\Big|=4$
$\Leftrightarrow \Big| \dfrac{(2m+1)^2}{m}\Big|=8$
$\Leftrightarrow \dfrac{(2m+1)^2}{|m|}=8$
$\Leftrightarrow 8|m|=4m^2+4m+1$
* Nếu $m>0$:
$4m^2+4m+1=8m$
$\Leftrightarrow 4m^2-4m+1=0$
$\Leftrightarrow (2m-1)^2=0$
$\Leftrightarrow m=\dfrac{1}{2}$ (TM)
* Nếu $m<0$:
$4m^2+4m+1=-8m$
$\Leftrightarrow 4m^2+12m+1=0$
$\Leftrightarrow m=\dfrac{-6\pm\sqrt{32}}{4}$ (TM)
