设函数 $F$ 连续可偏导，且 $z=z(x, y)$ 由 $F\left(x^2-z^2, y^2-z^2, x^2+y^2\right)=0$ 确定，则 $y \frac{\partial z}{\partial x}- x \frac{\partial z}{\partial y}=(\quad)$.
A
0
B
$\frac{x y\left(F_1^{\prime}-F_2^{\prime}\right)}{z\left(F_1^{\prime}+F_2^{\prime}\right)}$
C
$\frac{x y\left(F_1^{\prime}-F_3^{\prime}\right)}{z\left(F_1^{\prime}+F_2^{\prime}\right)}$
D
$\frac{x y\left(F_2^{\prime}-F_3^{\prime}\right)}{z\left(F_1^{\prime}+F_2^{\prime}\right)}$
E
F