2022 Putnam A1

Determine all ordered pairs of real numbers $(a,b)$ such that the line $y = ax+b$ intersects the curve $y = \ln(1+x^2)$ in exactly one point.

确定所有有序实数对 $(a,b)$，使得直线 $y = ax+b$ 与曲线 $y = \ln(1+x^2)$ 恰好相交于一个点。