Kör egyenlete: `(x-u)^2+(y-v)^2 = r^2`, ahol u,v a kör középpontjának a koordinátái, r pedig a sugara.

1) a) `(x+1)^2+(y-2)^2=1/5 Rightarrow x^2+2x+1+y^2-4y+4-1/5 = 0 Rightarrow x^2+y^2+2x-4y+24/5 = 0`

b) `(x+\sqrt{3})^2+(y+\sqrt{6})^2=4 Rightarrow x^2+2sqrt(3)x+3+y^2+2sqrt(6)y+6-4 = 0 Rightarrow x^2+y^2+2sqrt(3)x+2sqrt(6)y+5 = 0`

c) `(x+5)^2+(y+5)^2=25 Rightarrow x^2+10x+25+y^2+10y+25-25 = 0 Rightarrow x^2+y^2+10x+10y+25 = 0`

2) a) `x^2-4xcolor(red){+4}+y^2+8ycolor(red){+16}-16color(blue){-4}color(blue){-16} = 0 Rightarrow (x-2)^2+(y+4)^2-36 = 0 Rightarrow (x-2)^2+(y+4)^2 = 6^2`
`O(2;-4) \quad r=6`

b) `x^2-7xcolor(red){+(7/2)^2}+y^2+2ycolor(red){+1}-80color(blue){-(7/2)^2}color(blue){-1} = 0 Rightarrow (x-7/2)^2+(y+1)^2-373/4 = 0 Rightarrow (x-7/2)^2+(y+1)^2 = ((\sqrt{373})/2)^2`
`O(7/2;-1) \quad r=(sqrt(373))/2`

c) `x^2+3xcolor(red){+(3/2)^2}+y^2-5ycolor(red){+(5/2)^3}-25color(blue){-(3/2)^2}color(blue){-(5/2)^2} = 0 Rightarrow (x+3/2)^2+(y-5/2)^2-67/2 = 0 Rightarrow (x+3/2)^2+(y-5/2)^2 = (sqrt(67/2))^2`
`O(-3/2;5/2) \quad r=sqrt(67/2)`