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

Dear Varun

 

I am getting my answer as 3.

Please let me know if this is correct then I will share my solution.

 

let their be a line passing through (2,3) now let that line pass through (a,0) and point (0,b) now it forms a triangle with coordinate axis so 1/2*a*b=12 that implies that ab=24 now the equation of the line in intercept form is x/a+y/b=1 and now the equation passes through the point (2,3) and satisfies it so we get 3a+2b=24 (after putting ab=24 ) now the solution of this equation or the no. of values of a,b is the ans 
solutions:--------->
first ---->  a=6,b=3
second-----> a=4,b=6
third --------> a=2 ,b=9
so we have three lines obeying the conditions given in the question