Thank you for reporting, we will resolve it shortly
Q.
The number of possible straight lines, passing through $(2, 3)$ and forming a triangle with coordinate axes, whose area is 12 sq. units, is
Straight Lines
Solution:
Let line be $y - 3 = m (x - 2)$
$y$ intercept is $(3 - 2m), x$ intercept is $\left(2-\frac{3}{m}\right)$
Area $= 12$
$\therefore 12=\frac{1}{2}\left|2-\frac{3}{m}\right|\left|3-2m\right|$
$\Rightarrow 12-\frac{9}{m}-4m=+ 24$
$\therefore 4m^{2}+12m+9+0 \Rightarrow m=-3/2$
or $12-\frac{9}{m}-4m=-24 \Rightarrow 4m^{2}-36m+9=0; D > 0$