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. $\left(x-\sqrt{1-y^{2}}\right)\left(y+\sqrt{1-x^{2}}\right)=0$
The right half of the circle is given by the equation $x=\sqrt{1-y^{2}}$, and the lower half of the circle is given by the equation $y=-\sqrt{1-x^{2}}$. Therefore, the curve equation is $\left(x-\sqrt{1-y^{2}}\right)\left(y+\sqrt{1-x^{2}}\right)=0$, so the answer is $D$.