CIR018 · Circles · Classes 10–12
Circle Equations
A circle is every point at distance r from its centre (h, k). Pythagoras on the horizontal and vertical gaps gives its equation.
(x−h)²+(y−k)²Circle Equations
📐 Formula
(x − h)² + (y − k)² = r²
✏️ Worked example
Centre (1, 2), radius 3: (x − 1)² + (y − 2)² = 9.
🌍 Where it is used
GPS ranges, radar circles and designing wheels on a coordinate grid.
❓ Quick check
The centre of (x − 4)² + (y + 1)² = 16 is…
🏋️ Practice
EasyRadius of x² + y² = 25?
Answer: 5
MediumWrite the circle with centre (0, 3) and radius 2.
Answer: x² + (y − 3)² = 4
ChallengeFind centre and radius of x² + y² − 6x + 4y − 3 = 0.
Answer: Centre (3, −2), radius 4