= Solution
A stationary direction at the point has zero <directional derivative>, hence is perpendicular to $(1,2)$. The two opposite unit directions are
$$
\boxed{\hat{\mathbf t}=\pm\frac{(2,-1)}{\sqrt5}.}
$$
They are tangents to the circular <level curve>. “Stationary” here means zero first-order change. A finite straight move in a tangent direction gives squared radius $5+s^2$ and therefore a positive second-order change $\ln(1+s^2/5)$; following the curved level set instead keeps $T$ exactly constant.
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