[math-fun] Pythatgorean problem

I noticed that the 8-15-17 Pythagorean triangle, has 8 = 3+5 while 15 = 3*5, and then saw that the 3-4-5 triangle has 4 = 1+3 and 3 = 1*3. These turn out to be members of a family of Pythagorean triangles with a = x+(x+2), b = x(x+2), c = x(x+2)+2. Can all Pythagorean triangles with a = x+y, b = xy be parameterized?