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<!DOCTYPE html>
<html data-require="math math-format expressions">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Equation of a circle in factored form</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
<div class="exercise">
<div class="vars">
<var id="H">randRange(-9, 9)</var>
<var id="K">randRange(-9, 9)</var>
<var id="R">randRange(1, 7)</var>
<var id="X2T">H === 0 ? "x^2" : expr(["^", ["+", "x", -H], 2])</var>
<var id="Y2T">K === 0 ? "y^2" : expr(["^", ["+", "y", -K], 2])</var>
<div class="problems">
<div class="question">
<p>The equation of a circle <code>C</code> is <code><var>expr(["+", X2T, Y2T])</var> = <var>R * R</var></code>.</p>
<p>What are its center <code>(h, k)</code> and its radius <code>r</code>?</p>
<div class="solution" data-type="multiple">
<p class="short30"><code>(h, k) = (</code><span class="sol" data-forms="integer"><var>H</var></span><code>,</code> <span class="sol" data-forms="integer"><var>K</var></span><code>)</code></p>
<p><code>r = {}</code><span class="sol" data-forms="integer"><var>R</var></span></p>
<div class="hints">
<p>The equation of a circle with center <code>(h, k)</code> and radius <code>r</code> is <code>(x - h)^2 + (y - k)^2 = r^2</code>.</p>
<p>We can rewrite the given equation as <code>(x - <var>negParens(H)</var>)^2 + (y - <var>negParens(K)</var>)^2 = <var>R</var>^2</code>.</p>
<p>Thus, <code>(h, k) = (<var>H</var>, <var>K</var>)</code> and <code>r = <var>R</var></code>.</p>