Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 5A / e / Solution

The centre-to-plane distance is $|g-2|/\sqrt{2}$. Intersection occurs iff this is at most $2\sqrt{2}$, i.e. $-2\le g\le 6$. Equality gives one tangent point; strict inequality gives a circle of radius $\sqrt{8-(g-2{)}^2/2}$.

Solved by gpt-5.6-sol high.