<p>Find the centre and radius, then substitute into the standard equation.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 560px;"><colgroup><col style="width: 23.2143%;"><col style="width: 32.1429%;"><col style="width: 44.6429%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Given</strong></th><th style="text-align: center; --cell-justify: center"><strong>Method</strong></th><th style="text-align: center; --cell-justify: center"><strong>Example</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Centre and one point on the circle</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td><td class="table-cell--fill-in" style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center">Endpoints of a diameter</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td><td class="table-cell--fill-in" style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></div>
<p class="paragraph-header">Position of a point</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">\(d^2=(x_P-a)^2+(y_P-b)^2\)</p></div></div>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 540px;"><colgroup><col style="width: 50.0000%;"><col style="width: 50.0000%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Position</strong></th><th style="text-align: center; --cell-justify: center"><strong>Condition</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Inside</td><td style="text-align: center; --cell-justify: center">\(d^2&lt;r^2\)</td></tr><tr><td style="text-align: center; --cell-justify: center">On</td><td style="text-align: center; --cell-justify: center">\(d^2=r^2\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Outside</td><td style="text-align: center; --cell-justify: center">\(d^2&gt;r^2\)</td></tr></tbody></table></div></div>
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<p>For the diagram: \(CP^2=5&lt;16\), \(CQ^2=16\), \(CR^2=34&gt;16\).</p>

Find the centre and radius, then substitute into the standard equation.

\(r^2=\) squared distance from the centre to the point.

Centre \(=\) midpoint of the endpoints.
\(r^2=\) squared distance from the centre to either endpoint.

Given	Method	Example
Centre and one point on the circle
Endpoints of a diameter

Circles from Given Conditions and Position of a Point

Circles from Given Conditions and Position of a Point

Position	Condition
Inside	\(d^2<r^2\)
On	\(d^2=r^2\)
Outside	\(d^2>r^2\)