Parabola/ellipse tangents + area numerical
Knowledge bridge
Step 1: for the ellipse–parabola common-tangent MC, write both tangent conditions and compare. Step 2: later area NUM — find intersection limits first. Step 3: integrate difference of functions; keep trig-equation NUM technique nearby for neighbouring items.
Why it feels hard
Classic Advanced join: geometry conditions feeding calculus numerics in the same paper.
What to practise
Any week you revise conics, end with one area-between-curves NUM.