CIR019 · Circles · Classes 10–12
Coordinate circle
A circle centred at the origin with radius r is every point (x, y) with x² + y² = r², by Pythagoras on the right triangle under the radius.
x² + y² = r²Coordinate circle
📐 Formula
x² + y² = r²; point (r cos θ, r sin θ)
✏️ Worked example
r = 5: the point (3, 4) is on it because 9 + 16 = 25.
🌍 Where it is used
Computer graphics, GPS ranges, circular motion.
❓ Quick check
Is (6, 8) on x² + y² = 100?
🏋️ Practice
EasyRadius of x² + y² = 49?
Answer: 7
MediumIs (1, 2) on x² + y² = 4?
Answer: No (1 + 4 = 5)
ChallengeEquation of the circle centred at O through (5, 12)?
Answer: x² + y² = 169