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<!DOCTYPE html>
<html data-require="math math-format expressions interactive graphie">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Graphing circles</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div>
<div class="vars"
data-ensure="!(H === 0 && K === 0 && R === 2)">
<var id="H">randRange(-5, 5)</var>
<var id="K">randRange(-5, 5)</var>
<var id="R">randRange(1, 5)</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>
<p class="question">
Graph the circle <code><var>expr(["+", X2T, Y2T])</var>
= <var>R * R</var></code>.
</p>
<div class="problem">
<br>
<div class="graphie" id="grid">
graphInit({
range: 11,
scale: 20,
axisArrows: "&lt;-&gt;",
tickStep: 1,
labelStep: 1,
gridOpacity: 0.05,
axisOpacity: 0.2,
tickOpacity: 0.4,
labelOpacity: 0.5
});
label( [ 0, 11 ], "y", "above" );
label( [ 11, 0 ], "x", "right" );
addMouseLayer();
graph.circle = addCircleGraph();
</div>
</div>
<div class="solution" data-type="custom">
<div class="instruction">
Drag the center point and perimeter of the circle
to graph the equation.
</div>
<div class="guess">[
graph.circle.center[0],
graph.circle.center[1],
graph.circle.radius]
</div>
<div class="validator-function">
if (_.isEqual(guess, [0, 0, 2])) {
return "";
}
return _.isEqual(guess, [H, K, R]);
</div>
<div class="show-guess">
graph.circle.setCenter(guess[0], guess[1]);
graph.circle.setRadius(guess[2]);
</div>
</div>
<div class="hints">
<p>
The equation of a circle with center
<code>(\blue{h}, \green{k})</code> and radius
<code>\pink{r}</code> is
<code>(x - \blue{h})^2 + (y - \green{k})^2 =
\pink{r}^2</code>.
</p>
<p>
We can rewrite the given equation as
<code>(x - \blue{<var>negParens(H)</var>})^2 + (y -
\green{<var>negParens(K)</var>})^2 =
\pink{<var>R</var>}^2</code>.
</p>
<div>
<p>
Thus, the center of the circle should be
<code>(\blue{<var>H</var>}, \green{<var>K</var>})
</code> and the radius should be
<code>\pink{<var>R</var>}</code>.
</p>
<div class="graphie" data-update="grid">
circle([H, K], R, {
stroke: PURPLE,
strokeWidth: 1,
strokeDasharray: "- "
}).toBack();
</div>
</div>
</div>
</div>
</div>
</div>
</body>
</html>
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