Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

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 $12-\frac{9}{m}-4m=-24\Rightarrow 4m^2-36m+9=0;D>0$