let (h,k) be a fixed point , where h>0,k>0. a straight line passing through this point cuts the posi

let a and b be the intercepts made by the line on x and y axis.

equation of line will be

         (x/a)+(y/b)=1

the area of triangle made by this line will be (1/2)*a*b

since this line passes through (h,k). put it in that equation.then find the relation b/w a,b,h,k. replace b in terms of a,h,k in area expression. Then minimize it and find the value of a .

So min.area will occur when (h,k) is the middle point of the section of line intercepted b/w axis. in that case a=2h,b=2k

so min. area will be=2hk