MM3: Coordinate Geometry of Circles and Lines
Official Cambridge & Imperial ESAT specification requirements for Coordinate Geometry of Circles and Lines on the Mathematics 2 paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.
Official Syllabus Subtopics
Requirements specified in the UAT-UK framework
- 1Standard circle equation: (x - a)² + (y - b)² = r²
- 2Completing the square in two variables to extract centre and radius
- 3Tangent-radius perpendicularity condition: m(tan) × m(rad) = −1
- 4Perpendicular distance from a point to a line
- 5Line-circle intersection via discriminant condition Δ = 0 for tangency
- 6Extremal distances from an external point to a circle: d(centre) ± r
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
A line is tangent to a circle if the discriminant of their intersection equation is Δ = 0.
The shortest distance from an external point (x₀, y₀) to a circle is distance(centre, point) - r.
Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.
Tested Topics in Specification MM3
Master the individual question patterns and Sub-90 shortcuts for this specification.
Circle Coordinate Geometry, Tangent Discriminants & Extremal Distances
Never substitute y = mx + c into a circle if you can use geometry: a line is tangent iff perpendicular distance from centre (a,b) equals radius r, and shortest distance to an external point P is |CP| - r.
Ready to Master Specification MM3 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.