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

Equation of line xa+yb=1 , through (2,3)⇒ 2a+3b=1⇒2b+3a=ab  area =12|ab|=12|ab|=24⇒ab=±24 When ab=242b+3a=24⇒ 2ab+3a2=24a⇒ 3a2−24a+48=0⇒ a2−8a+16=0⇒ a=4⇒b=6 When ab=−24⇒ 2b+3a=−24⇒ a2+8a−16=0Two values of a. Hence 3 straight lines.