<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-graphing-circles">Graphing Circles Exercise</a></p><p><span style="color:#27ae60;">Graphic Circles</span> is pretty straightforward if your equation is in the general format, as seen below:</p>
<p>$$r^2 = (x-h)^2 + (y-k)^2$$</p>
<p>Where:</p>
<ul>
<li>$(h,k)$ is the circle's center</li>
<li>$r$ is the radius of the circle</li>
<li>$(x,y)$ represent poins on the circle</li>
</ul>
<p><strong><span style="color:#8e44ad;">Example</span></strong></p>
<p>$$16 = (x-5)^2 + (y+2)$$</p>
<p>The radius of the circle above is $4$ and the center is $(5, -2)$.</p>
<p><strong><span style="color:#8e44ad;">What if it's not in the general format?</span></strong></p>
<p>You likely have to complete the square (maybe even twice) to get it into the general format. See below:</p>
<p>$$3 = x^2 +4x + y^2 -6y$$</p>
<p>We have to complete the square twice, once for the $x$ and once for the $y$.</p>
<p>$$3 + 4 + 9 = (x^2 +4x +4) + (y^2 -6y + 9)$$</p>
<p>$$16 = (x+2)^2 + (y-3)^2$$</p>
<p>Amazeballs.</p>