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

Step-by-step solution

Let the equation of the line be x a + y b =1 Since line passes through the point (2,3) , we get 2 a + 3 b =1 2 b+3 a=a b As per the given condition, Area of the triangle =12 sq. units array ll & 1 2 |a b|=12 & a b= 24 & Case I : & ab =24 & 2 b+3 a=24...(ii) & 2 24 a ^2+3 a=24 ...[from (i)] & 16=8 a ...[from (ii)] & a^2-8 a+16=0 & a=4 & b=6 array array ll & Case II : & a b=-24 & 2 ( -24 a )+3 a=-24 & a^2+8 a-16=0 & a= -8 64+64 2 =-4 4 2 array ...[from (i) and (ii)] b will also have 2 values. The required number of l