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

Let  m be the slope of the line passing through (2, 3)

Equation of a line

Y – 3 = m ( x – 2 )

mx – y + 3 – 2m = 0

Given Area with co-ordinate axis is 12

$\begin{array}{l}\Rightarrow \frac{{\left(3-2m\right)}^2}{2\left|mx-1\right|}=12\\ \Rightarrow 9+4m^2-12m=24m\\ \Rightarrow 4m^2-36m+9=0\\ \Rightarrow \Delta =b^2-4ac={\left(36\right)}^2-4\left(4\right)9=1296-144=1152>0\\ \therefore mhastwovalues\\ \therefore No.oflinesare\left(2\right)\end{array}$