how we can find incentre if the incircle is made by x,y axis and a line having intercepts a and b as a/x+b/y = 1.

Dear student,

given equation has intercept a and b. The angular bisector of O is y=x

the angular bisector of of other vertex has slope equal to tan(180 - (1/2)tan^-1 (b/a)) let us call this as m

and this passes through a,0 and equation is y = mx - ma

put x=y in the equation

=> incentre = x,y = -ma/1-m,-ma/1-m