The number of possible straight lines passing through the point (2,3) , while forming a triangle with coordinate axes enclosing an area 12 sq. units is

Step-by-step solution

Let the equation of line forming a triangle having area 12 sq . units is x a + y b =1 So, |a b|=24 Line (i) passes through point (2,3) , so 2 a + 3 b =1 from Eqs. (ii) and (iii), we get |2 b+3 a|=24 If a and b are positive, then array rlrl & & a b=24 and 3 a+2 b=24 & a ( 24-3 a 2 )=24 & 3 a^2-24 a+48=0 & Discriminant =24^2-4 3 48=0 & a=4 and b=6 array If a is positive and b is negative then a b=-24 and 3 a+2 b=24 . 2 ( 24-3 a 2 )=-24 3 a^2-24 a-48=0 Discriminant =24^2+4 3 48>0 array ll a= 24 2 24^2 6 =4+4 2 a>0 and