A circle consists of points a distance r>0 from its centre (a,b). (x-a)2+(y-b)2=r2 General form x2+y2+2gx+2fy+c=0 Centre (-g,-f) and radius sqrt(g2+f2-c), where g2+f2-c>0. Complete the square in x and y to find the centre and radius. **Step** | **Working** Group the x-terms and the y-terms. | x2+y2-10x+6y+18=0 (x2-10x)+(y2+6y)+18=0 Complete each square. | (x-5)2-25+(y+3)2-9+18=0 Collect the constants on the right. | (x-5)2+(y+3)2=16 Read off the centre and the radius. | Centre (5,-3) Radius =sqrt(16)=4 Read the centre with opposite signs; the right side is r2>0.

A circle consists of points a distance \(r>0\) from its centre \((a,b)\).

Centre \((-g,-f)\) and radius \(\sqrt{g^2+f^2-c}\), where \(g^2+f^2-c>0\).

Complete the square in x and y to find the centre and radius.

Group the \(x\)-terms and the \(y\)-terms.

\(\begin{aligned} x^2+y^2-10x+6y+18&=0 \\ (x^2-10x)+(y^2+6y)+18&=0 \end{aligned}\)

Equation of Circle

Equation of Circle