Support · Mathematics Advanced 11–12 – Year 11 · Graph transformations
Support Find the centre and radius of circles of the form x² + y² + ax + by + c = 0, where a, b and c are constants, by completing the squares
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
Prerequisite links are draft mappings generated from the syllabus structure (earlier stage, same strand, closest content). They are being reviewed by teachers. Spot a poor match? Tell us.
Prerequisite dot points
Find the centre and radius of a circle with the equation in the form x² + y² + ax + by + c = 0 by completing the square
Stage 5 · Non-linear relationships C (Path) Draft mapping
- Interactive toolStarterMaths Is Fun: Equation of a circleUse it for: Derives x² + y² = r² from Pythagoras, with an interactive.
- WorksheetDrillKuta free worksheet: Equations of circlesUse it for: Printable skills-practice sheet with answer key on equations of circles; good for drill or homework.
Establish the equation of the circle with centre (a,b) and radius r, and graph equations of the form (x - a)² + (y - b)² = r²
Stage 5 · Non-linear relationships C (Path) Draft mapping
- Interactive toolStarterMaths Is Fun: Equation of a circleUse it for: Derives x² + y² = r² from Pythagoras, with an interactive.
- WorksheetDrillKuta free worksheet: Equations of circlesUse it for: Printable skills-practice sheet with answer key on equations of circles; good for drill or homework.
Graph circles of the form x² + y² = r², where r is the radius of the circle using graphing applications
Stage 5 · Non-linear relationships C (Path) Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- WorksheetDrillKuta free worksheet: Graphing circlesUse it for: Printable skills-practice sheet with answer key on graphing circles; good for drill or homework.