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Circle Equations

Circle Equations

Circle centered at (x0, y0) with radius r, a point P(x, y) on the circle, and angle t

1. Centre-radius form:

Circle having centre (x0, y0) and radius r.

The equation of the circle can be represented as:

(x-x0)^2 + (y-y0)^2 = r^2

General Equation of a Circle:

x^2 + y^2 + 2gx + 2fy + c = 0

where, g, f, and c are constants.

Therefore,

x0 = (-g), y0 = (-f), and r = square root of (g^2 + f^2 -c)

2. Parametric form:

Circle having centre (x0, y0) and radius makes an angle t with the positive direction of x-axis, then t is called the parameter.

The equation of the circle can be represented as:

x = x0 + rcos(t), y = y0 + rsin(t)

for,

0<=t<= 2 pi

More Information:

Equation of a Circle