The number of possible straight lines, passing through (2, 3) and forming a triangle with coordinate axes, whose area is 12 sq. units is_

$\text{ Equation of any line through }(2,3)\text{ is }y-y_1=m\left(x-x_1\right)$

$y-3=m(x-2)$

$\Rightarrow \frac{x}{\frac{2m-3}{m}}+\frac{y}{3-2m}=1$

$\text{ Since, Area of }\Delta OAB=12$

$\Rightarrow \frac{1}{2}\left|ab\right|=12$

$\Rightarrow \frac{1}{2}\left(\frac{2m-3}{m}\right)(3-2m)=\pm 12$

$\text{ Taking positive sign, we get }m=-\frac{3}{2}$

$\text{ Taking negative sign, we get }4m^2-36m+9=0$

$\text{ And }\Delta >0\Rightarrow m\text{ has two values }$

Hence, three straight lines are possible