If the line \(y=x\) is a tangent to the parabola \(y=a x^{2}+b x+c\) at the point \((1,1)\) and the curve passes through \((-1,0)\), then
(A) \(a=b=-1, c=3\)
(B) \(a=b=\frac{1}{2}, c=0\)
(C) \(a=c=\frac{1}{4}, b=\frac{1}{2}\)
(D) \(a=0, b=c=\frac{1}{2}\)