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

Answer 1

Answer: 3

Let line be $y-3=m(x-2)$
$y$ intercept is $(3-2m),x$ intercept is $(2-\frac{3}{m})$
Area $=12$
$\therefore 12=\frac{1}{2}|2-\frac{3}{m}||3-2m|$
$\Rightarrow 12-\frac{9}{m}-4m=24$
$\therefore 4m^2+12m+9=0$
$\Rightarrow m=-3/2$
or $12-\frac{9}{m}-4m=-24$
$\Rightarrow 4m^2-36m+9=0$
$D>0$
$\Rightarrow$ There are two values of $m$.
Hence, total $3$ values of $m$.