{x/y -y/x=24/5; t=x/y; x≠0; y≠0
{x^2+y^2=1664
t-1/t=24/5; t^2 -1=24/5 t; D1==(12/5)^2+1=144/25+1=169/25=(13/5)^2; t1=-12/5+13/5=1/5; t2=-12/5-13/5=-5
x/y=1/5; x=0,2y. (0,2y)^2 +y^2=1664; 1,04y^2=1664; y^2=1600; y=+-40
y=40; x^2=1664-1600; x^2=64; x=+-8; (8;40); (-8;40)
x/y=-5; x=-5y; (-5y)^2+y^2=1664; 26y^2=1664; y^2=64; y=+-8;
y=-8; x=-5*(-8)=40; (40;-8); (-40;8)
y=8; x=-5*8=-40
Ответ. (-8;40); (8;40); (40;-8);(-40;8)