What you need to know
Check yourself against these “I can” statements.
- I can explain why (x − a)² + (y − b)² = r² is a circle with centre (a, b) and radius r (Further Maths)
- I can write the equation of a circle from its centre and radius (Further Maths)
- I can find the centre and radius of a circle from its equation (Further Maths)
- I can find the equation of a tangent to a circle (Further Maths)
Practise this topic
6 resourcesCircle Geometry (GCSE Further Maths)
The equation of a circle for AQA Level 2 Further Maths, with GCSE-friendly numbers: centre, radius and equation; completing the square; the equation from a diameter or a centre and a point; points inside, on or outside and the…
⚙️ WorksheetEquation of a Circle: Fill in the Blanks
A table of circles: each row gives the expanded equation, the (x − a)² + (y − b)² = r² form, or the centre and radius; fill in the rest. Surd radii, rearranged equations and non-circles on higher levels.
🧮 ToolCircle Explorer
Drag a circle’s centre and radius on a large coordinate grid and see its equation in both forms, with the working for completing the square (or type an equation in either form). Points inside, on or outside, shortest and longest…
⬢ BlockbustersCircle Geometry (GCSE Further Maths) Blockbusters
Blockbusters with the questions from the Circle Geometry (GCSE Further Maths) worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer…
🔤 Fill the GapsFill the Gaps: Maths Vocabulary
A sentence explaining one of the unit’s key words, with gaps. Pick the right word for each gap from the words scattered round it: the right ones and plenty of wrong ones. A deck for every unit.
🧮 ToolGraph Plotter
A graphing calculator: type y = f(x), x = g(y), implicit relations such as x² + y² = 25, inequalities (shaded, dashed for < and solid for ≤), parametric and polar curves, points and tables, functions f(x) = … with f′(x), and…
These are the pages for Circle Equations in the GCSE + AQA Further Maths scheme of work, following Pearson Edexcel GCSE (9–1) Higher (1MA1), plus AQA Level 2 Further Mathematics (8365). Open this topic in Mr Wells Maths to see it alongside the rest of the course.