In keynote 4, example 2, total non-negative unordered integral solutions is just 1 (4,0) and total non-negative ordered integral solutions are 2 (4,0 and 0,4). Please Correct me if I'm wrong.

@raman_sharma
BC =1 , CA =2 so AB =rt5using similarity in triangle ABC and ADCwe get CD= 2/rt5 and diameter of circle as 4/rt5
now using tangent secant theoremCD^2 = CE * AC4/5 = CE *2CE =0.4so AE=1.6hence 1.6/0.4 = 4