Coordinate geometry in the TMUA is visual algebra: lines, circles and parabolas described, intersected and sketched. Core moves are gradient and equation of a line through two points, circle centre-radius form, intersection of line and curve (substitute and solve — discriminant tells the story), and tangents via perpendicular gradients or differentiation.
Sketches earn marks indirectly: intercepts, symmetry and asymptotes eliminate options before any algebra. The recurring trap is asserting tangency from a diagram alone — always verify algebraically, and keep centre-radius completing-the-square fluent.
Study method: attempt five timed questions, log every miss with its topic code, redo misses from scratch within 48 hours, then re-attempt the topic a week later. Pair each hub with its drill link below and a fortnightly full mock.
Place this topic in the wider test with the syllabus checklist and Paper 1 vs Paper 2, learn the timing system in how to prepare, and check what scores mean in scores explained.