Formulas & tables/Mathematics/Analytic geometry/Equation of a circle

Equation of a circle

(x−a)2+(y−b)2=r2(x-a)^2+(y-b)^2=r^2

Result unit: — (circle equation)

What it describes

The equation of a circle with center (a,b)(a,b) and radius rr.

Symbols

(a,b)(a,b)
center of the circle
rr
radius
x,yx, y
coordinates of a point

Where it comes from

A circle is the set of points at distance rr from the center (a,b)(a,b) — the formula follows directly from the definition of distance.

When to use it

Circles in the coordinate system; intersections with a line, tangents.

Example

Center (2,3)(2,3), radius 5. Give the equation of the circle.
Substitutiona=2a=2, b=3b=3, r=5r=5.
Result(x−2)2+(y−3)2=25(x-2)^2+(y-3)^2=25.

Related formulas

Midpoint of a segment Distance between two points

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