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Circles - Coggle Diagram
Circles
general equation
x^2 + y^2 +2gx+2fy+c=0
center = (-g,-f)
radius = √(g^2+f^2-c)
make coeff. of x^2 and y^2 =0
coeff. of xy=0
parametric form
when circle is at (0,0)
x= r cos Q y= r sinQ
when circle is at A(x1,y1)
x= x1+r cosQ y= y1+ r sin Q
intercept of axes
x axis = 2√(g^2-C)
y axis =2√(f^2-C)
center radius form
(x-x1)^2 + (y-y1)^2 = r^2
passing through origin
x^2+y^2 + 2gx+2fy=0
centered at x axis
x^2+Y^2+2gx+c=0
centered at y axis
x^2+y^2+2fy+c=0
equation of circle touching both the axes
(x±r)^2+(y±r)^2=r
diametric form
(x-x1)(x-x2)+(y-y1)(y-y2)=0