Giả sử A là điểm có hoành độ âm
\(A\left(x_A;y_A\right);B\left(x_B;y_B\right);C\left(x_A;0\right);D\left(x_B;0\right)\)
\(\Rightarrow S_{OAB}=S_{ACDB}-S_{OAC}-S_{OBD}\)
\(\Rightarrow S_{OAB}=\frac{1}{2}\left(y_A+y_B\right)\left(x_B-x_A\right)-\frac{1}{2}y_A\left(-x_A\right)-\frac{1}{2}y_Bx_B\)
\(\Rightarrow S_{OAB}=\frac{1}{2}\left(y_Ax_B-y_Ax_A+y_Bx_B-y_Bx_A+x_Ay_A-x_By_B\right)\)
\(\Rightarrow S_{OAB}=\frac{1}{2}\left(y_Ax_B-y_Bx_A\right)=\frac{1}{2}\left(x_B\left(mx_A+1\right)-x_A\left(mx_B+1\right)\right)\)
\(\Rightarrow S_{OAB}=\frac{1}{2}\left(x_B-x_A\right)=2\Rightarrow x_B-x_A=4\)
Kết hợp Viet ta có hệ: \(\left\{{}\begin{matrix}x_A+x_B=m\\x_B-x_A=4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_B=\frac{m+4}{2}\\x_A=\frac{m-4}{2}\end{matrix}\right.\)
\(x_Ax_B=-1\Rightarrow\left(\frac{m-4}{2}\right)\left(\frac{m+4}{2}\right)=-1\)
\(\Rightarrow m^2-16=-4\Rightarrow m^2=12\Rightarrow m=\pm2\sqrt{3}\)
