<p>A circle consists of points a distance \(r&gt;0\) from its centre \((a,b)\).</p>
<div class="content-box-placement content-box-placement--full content-box-placement--align-center" style="display:flex;justify-content:stretch;max-width:100%"><div class="content-box content-box--emphasis" data-content-box-preset="emphasis" style="box-sizing:border-box;border-color:var(--content-box-border, #1E6FBA);border-style:solid;border-width:0px;border-radius:0px;background-color:var(--content-box-background, #F5F8FC);color:var(--content-box-foreground, #111827);padding:12px 16px;font-family:'EB Garamond', serif;font-size:16px;line-height:1.35;width:100%;max-width:100%;border-left-width:3px"><p style="text-align: center">\((x-a)^2+(y-b)^2=r^2\)</p></div></div>
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<p class="paragraph-header">General form</p>
<div class="content-box-placement content-box-placement--full content-box-placement--align-center" style="display:flex;justify-content:stretch;max-width:100%"><div class="content-box content-box--emphasis" data-content-box-preset="emphasis" style="box-sizing:border-box;border-color:var(--content-box-border, #1E6FBA);border-style:solid;border-width:0px;border-radius:0px;background-color:var(--content-box-background, #F5F8FC);color:var(--content-box-foreground, #111827);padding:12px 16px;font-family:'EB Garamond', serif;font-size:16px;line-height:1.35;width:100%;max-width:100%;border-left-width:3px"><p style="text-align: center">\(x^2+y^2+2gx+2fy+c=0\)</p></div></div>
<p>Centre \((-g,-f)\) and radius \(\sqrt{g^2+f^2-c}\), where \(g^2+f^2-c&gt;0\).</p>
<p>Complete the square in x and y to find the centre and radius.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 540px;"><colgroup><col style="width: 40.7407%;"><col style="width: 59.2593%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Step</strong></th><th style="text-align: center; --cell-justify: center"><strong>Working</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Group the \(x\)-terms and the \(y\)-terms.</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Complete each square.</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Collect the constants on the right.</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Read off the centre and the radius.</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr></tbody></table></div></div>
<p>Read the centre with opposite signs; the right side is \(r^2&gt;0\).</p>

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

Step	Working
Group the \(x\)-terms and the \(y\)-terms.
Complete each square.
Collect the constants on the right.
Read off the centre and the radius.