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

The equation of any line through 2,3 is y−3=mx−2or y=mx−2m+3From the figure, the area of ΔOAB is ±12, that is, 122m−3m3−2m=±12Taking positive sign, we get 2m+32=0. This gives one value of m as -3/2. Taking negative sign, we get4m2−36m+9=0D>0This is a quadratic in m which gives two values of m. Hence, three straight lines are possible.