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      <text>17.1.1.3 The circle</text>
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      <text><![CDATA[<h3> The circle </h3>
The circle is a special case of the ellipse; it occurs when \(a=b=r\) so the equation becomes
<br>\[\frac{x^2}{r^2}+\frac{y^2}{r^2}=1\qquad \text{or, more commonly}\quad x^2+y^2=r^2.\]<br>Here, the <strong>centre</strong> of the circle is located at the origin \((0,0)\) and the <strong>radius</strong> of the circle is \(r\). If the centre of the circle at a point \((\alpha ,\beta )\) then the equation takes the form:
<br>\[(x-\alpha)^2+(y-\beta)^2=r^2\]<br><div class="HELM_keypoint">
<h4>Key Point</h4>
<p>The equation of a circle with centre at \((\alpha,\beta)\) and radius \(r\) is \[(x-\alpha)^2+(y-\beta)^2=r^2.\]</p>
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