Question 16
(YUG 2) Determine all triples $(a,b,c)$ of positive real numbers such that the system
$$ax+by-cz=0,$$
$$a\sqrt{1-x^2}+b\sqrt{1-y^2}-c\sqrt{1-z^2}=0$$
is compatible in the real numbers, and then find all its real solutions.
$$ax+by-cz=0,$$
$$a\sqrt{1-x^2}+b\sqrt{1-y^2}-c\sqrt{1-z^2}=0$$
is compatible in the real numbers, and then find all its real solutions.