EquationEquation GraphGraph CentreCentre RadiusRadius
x2+y2=a2x^2+y^2=a^2 (0,0)(0,0) aa
(xh)2+(yk)2=a2(x-h)^2+(y-k)^2=a^2 (h,k)(h,k) aa
x2+y2+2gx+2fy+c=0x^2+y^2+2gx+2fy+c=0 (g,f)(-g,-f) g2+f2c\sqrt{g^2+f^2-c}

Equations of Tangent of all Circles

Equations ofEquations\space of
CircleCircle
Point/Line of contact of Point/Line\space of\space contact\space of \space
circlecircle
 m=slope of tangent\ m=slope \space of \space tangent
Equation of Equation\space of\space
tangent tangent
x2+y2=a2x^2+y^2=a^2 (x1,y1)(x1,y1) xx1+yy1=a2xx1 +yy1=a^2
x2+y2=a2x^2+y^2=a^2 (a cosθ,b sinθ)(a \space cos\theta,b \space sin\theta) x cosθ+y sinθ=ax \space cos\theta + y \space sin\theta=a
x2+y2=a2x^2+y^2=a^2 y=mx+cy=mx+c y=mx±a1+m2y=mx±a\sqrt{1+m^2}
x2+y2+2gx+2fy+c=0x^2+y^2+2gx+2fy+c=0 (x1,y1)(x1,y1) xx1+yy1+g(x+x1)+f(y+y1)+c=0xx1+yy1+g(x+x1)+f(y+y1)+c=0

Equations of Normal of all Circles

Equations ofEquations\space of
CircleCircle
Point/Line of contact of Point/Line\space of\space contact\space of \space
circlecircle
 m=slope of tangent\ m=slope\space of \space tangent
Equation of Equation\space of\space
 Normal\ Normal
x2+y2=a2x^2+y^2=a^2 (x1,y1)(x1,y1) xx1=yy1\frac{x}{x1}=\frac{y}{y1}
x2+y2=a2x^2+y^2=a^2 (a cosθ,b sinθ)(a \space cos\theta,b \space sin\theta) y=x tanθy=x\space tan\theta
x2+y2=a2x^2+y^2=a^2 y=mx+cy=mx+c x+my=±a1+m2x+my=±a\sqrt{1+m^2}
x2+y2+2gx+2fy+c=0x^2+y^2+2gx+2fy+c=0 (x1,y1)(x1,y1) yy1xx1=y1+fx1+g\frac{y-y1}{x-x1}=\frac{y1+f}{x1+g}

Director Circle of all Circles

Equations of CircleEquations\space of\space Circle Equation of Director CircleEquation\space of\space Director\space Circle
x2+y2=a2x^2+y^2=a^2 x2+y2=2 a2x^2+y^2=2 \space a^2
(xh)2+(yk)2=a2(x-h)^2+(y-k)^2=a^2 (xh)2+(yk)2=2 a2(x-h)^2+(y-k)^2=2 \space a^2
x2+y2+2gx+2fy+c=0x^2+y^2+2gx+2fy+c=0 (x+g)2+(y+f)2=2(g2+f2c)(x+g)^2+(y+f)^2=2(g^2+f^2-c)