Paper 2 · Co-ordinate Geometry of the Circle ⏱ Tested in 5 exam questions since 2024 Lesson 2 of 9

The Circle 2 – Characteristics of the equation of a circle

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You’ll learn

Check the two circle diagnostics: equal x² and y² coefficients, and no xy term
Spot non-circles: x² − y² (hyperbola), 2x² + y² (ellipse), any xy term
Divide the whole equation by the leading coefficient before using page-19 formulas

2025 Paper 2 Q2(a)(i) — standard form of a circle: (x − h)² + (y − k)² = r² has centre (h, k) and radius r
2025 Paper 2 Q6(a)(i) — convert the general form x² + y² + 2gx + 2fy + c = 0 of a circle to centre (−g, −f) and…
2024 Paper 2 Q2(a) — circle equation from centre + one point — radius equals the distance from the centre to…
2024 Paper 2 Q2(b) — symmetries of a circle — any point obtained by reflecting a known point through the cent…
2024 Paper 2 Q5(a)(i) — general form of a circle: x² + y² + 2gx + 2fy + c = 0 has centre (−g, −f) and radius √(g…

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