The Circle — Formula Sheet

Circle = locus of all points in a plane equidistant from a fixed point

Standard Equation of a Circle: (x-h)^2+(y-k)^2=r^2

Equation of circle centred at origin: x^2+y^2=r^2

General Equation of a Circle: x^2+y^2+2gx+2fy+c=0

Diameter Equation of a Circle: (x-x1)(x-x2)+(y-y1)(y-y2)=0

If centre is (0,2) and radius is 2, then x^2+(y-2)^2=4

If centre is (-2,3) and radius is 4, then (x+2)^2+(y-3)^2=16

If centre is (0,0) and radius is a, then x^2+y^2=a^2

If centre is (-a,-b) and radius is sqrt(a^2-b^2), then x^2+y^2+2ax+2by+2b^2=0

Centre of x^2+y^2-6x+4y-12=0 is (3,-2)

For 2x^2+2y^2+3x+4y+9/8=0, divide by 2 first

If diameter endpoints are (1,3) and (4,5), equation is (x-1)(x-4)+(y-3)(y-5)=0

The standard equation of a circle with centre (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.

If the centre is at the origin, the equation becomes x^2 + y^2 = r^2.

The general equation of a circle is x^2 + y^2 + 2gx + 2fy + c = 0.

The equation is (x-x1)(x-x2) + (y-y1)(y-y2) = 0.

Radius = sqrt(g^2 + f^2 - c).

The general equation is x^2+y^2+2gx+2fy+c=0.

If the end-points of a diameter are (x1,y1) and (x2,y2), then the circle is given by (x-x1)(x-x2)+(y-y1)(y-y2)=0.

A circle with centre (h,k) and radius r can be written as x=h+r cosθ and y=k+r sinθ, where 0≤θ<2π.