Question

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

• A. $One$
• B. $Two$
• C. $Three$
• D. $Four$

Answer 1

The correct option is C $Three$

Equation of any line through $(2,3)$ is
$y-3=m(x-2)$

$\Rightarrow y=mx-2m+3$

Given, area of $\Delta$OAB is $\pm 12.$ That is,

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

Taking positive sign, we get $(2m+3{)}^2=0$. This gives one value of m as

$\frac{-3}{2}$.

Taking negative sign, we get

$4m^2-36m+9=0(D>0)$

This is a quadratic in $m$ which gives two real values of $m.$

Hence, three straight lines are possible.