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Given : $$x^2 = 2 - y^2$$
=> $$x^2+y^2=2$$ ----------(i)
Also, $$x=1-y$$
=> $$x+y=1$$
Squaring both sides, we get :
=> $$(x+y)^2=(1)^2$$
=> $$(x^2+y^2)+2xy=1$$
=> $$2+2xy=1$$ [Using (i)]
=> $$2xy=1-2=-1$$
=> $$xy=\frac{-1}{2}$$
=> Ans - (C)
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