2. Given that the curve in the figure is part of a circle centered at the origin with a radius of 1, the equation of this curve is
(A) $\left(x+\sqrt{1-y^{2}}\right)\left(y+\sqrt{1-x^{2}}\right)=0$
(B) $\left(x-\sqrt{1-y^{2}}\right)\left(y-\sqrt{1-x^{2}}\right)=0$
(C) $\left(x+\sqrt{1-y^{2}}\right)\left(y-\sqrt{1-x^{2}}\right)=0$
(D) $\left(x-\sqrt{1-y^{2}}\right)\left(y+\sqrt{1-x^{2}}\right)=0$
(D)
2.【Analysis and Solution】Since the curve is the union of the right half of the unit circle and the lower half of the unit circle, the equation of the right half of the unit circle is $x-\sqrt{1-y^{2}}=0$, and the equation of the lower half of the unit circle is $y+\sqrt{1-x^{2}}=0$.