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<quiz>
  <question type="stack">
    <name>
      <text>2.6.3.1 Find centre and radious</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Write down the radius and the coordinates of the centre of the circle for each of the following equations</p>

<ol class="HELM_parts">
    <li>
        <p>{@c1@}</p>
        <p>\( C \big ( \) [[input:ans1]] [[validation:ans1]],[[input:ans2]] [[validation:ans2]] \( \big) \) [[feedback:prtC1]]</p>
        <p>\( r= \)[[input:ans3]] [[validation:ans3]] [[feedback:prtR1]]</p>
    </li>

    <li>
        <p>{@c2@}</p>
        <p>\( C \big ( \) [[input:ans4]] [[validation:ans4]],[[input:ans5]] [[validation:ans5]] \( \big) \) [[feedback:prtC2]]</p>
        <p>\( r= \)[[input:ans6]] [[validation:ans6]] [[feedback:prtR2]]</p>
    </li>

    <li>
        <p>{@c3@}</p>
        <p>\( C \big ( \) [[input:ans7]] [[validation:ans7]],[[input:ans8]] [[validation:ans8]] \( \big) \) [[feedback:prtC3]]</p>
        <p>\( r= \)[[input:ans9]] [[validation:ans9]] [[feedback:prtR3]]</p>
    </li>

    <li>
        <p>{@c4@}</p>
        <p>\( C \big ( \) [[input:ans10]] [[validation:ans10]],[[input:ans11]] [[validation:ans11]] \( \big) \) [[feedback:prtC4]]</p>
        <p>\( r= \)[[input:ans12]] [[validation:ans12]] [[feedback:prtR4]]</p>
    </li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li>
        <p>For the circle {@c1@}</p>
        <p>Centre: \( ({@x1@}, {@y1@})\) </p>
        <p>Radious \( r= \sqrt{ {@r1^2@} } = {@r1@}\)</p>
    </li>

    <li>
        <p>For the circle {@c2@}</p>
        <p>Centre: \( ({@x2@}, {@y2@})\) </p>
        <p>Radious \( r= \sqrt{ {@r2^2@} } = {@r2@}\)</p>
    </li>

    <li>
        <p>For the circle \({@c3@} \Rightarrow {@(x-x3)^2+(y-y3)^2@} = {@r3^2@}\)</p>
        <p>Centre: \( ({@x3@}, {@y3@})\) </p>
        <p>Radious \( r= \sqrt{ {@r3^2@} } = {@r3@}\)</p>
    </li>

    <li>
        <p>For the circle \({@c4@} \Rightarrow {@(x-x4)^2+(y-y4)^2@} = {@r4^2@}\)</p>
        <p>Centre: \( ({@x4@}, {@y4@})\) </p>
        <p>Radious \( r= \sqrt{ {@r4^2@} } = {@r4@}\)</p>
    </li>
</ol>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2021120900</text>
    </stackversion>
    <questionvariables>
      <text>ordergreat (x,y);
/* Define centre and radius*/
x1: 0;
y1:0;
r1: rand([3,4,5]);
x2: -rand([2,3,4,5]);
y2: rand([1,2]);
r2: rand_with_prohib(3,6,[r1]);
x3: 0;
y3: -rand([1,2]);
r3: rand([2,3,4]);
x4: -rand([5,6,7]);
y4: 0;
r4: rand([5,6,7]);

c1: (x-x1)^2+(y-y1)^2= r1^2;
c2: (x-x2)^2+(y-y2)^2= r2^2;
c3: (x-x3)^2+(y-y3)^2- r3^2=0;
c4: (x-x4)^2+(y-y4)^2- r4^2=0;</text>
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      <text/>
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    <questionnote format="moodle_auto_format">
      <text>\[{@c1@}, \quad {@c2@} \]
\[{@c3@}, \quad {@c4@} \]</text>
    </questionnote>
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      <text/>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
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    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
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        <falsefeedback format="html">
          <text><![CDATA[<p dir="ltr" style="text-align: left;">The \( y\)&nbsp; coordinate is incorrect.<br></p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans11</sans>
        <tans>y4</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.5000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prtC4-3-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prtC4-3-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p dir="ltr" style="text-align: left;">The \( y\)&nbsp; coordinate is incorrect.<br></p>]]></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prtR1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans3</sans>
        <tans>r1</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prtR1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prtR1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prtR2</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans6</sans>
        <tans>r2</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prtR2-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prtR2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prtR3</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans9</sans>
        <tans>r3</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prtR3-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prtR3-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prtR4</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans12</sans>
        <tans>r4</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prtR4-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prtR4-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>720523260</deployedseed>
    <deployedseed>1435879291</deployedseed>
    <deployedseed>228774487</deployedseed>
    <deployedseed>1556333244</deployedseed>
    <deployedseed>794540637</deployedseed>
    <deployedseed>1864476365</deployedseed>
    <deployedseed>2136615010</deployedseed>
    <deployedseed>1289774214</deployedseed>
    <deployedseed>1141627684</deployedseed>
    <deployedseed>671728823</deployedseed>
    <deployedseed>628271163</deployedseed>
    <deployedseed>285089188</deployedseed>
    <deployedseed>1191612503</deployedseed>
    <deployedseed>101697902</deployedseed>
    <deployedseed>795813395</deployedseed>
    <deployedseed>2070213731</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>x1</value>
      </testinput>
      <testinput>
        <name>ans10</name>
        <value>x4</value>
      </testinput>
      <testinput>
        <name>ans11</name>
        <value>y4</value>
      </testinput>
      <testinput>
        <name>ans12</name>
        <value>r4</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>y1</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>r1</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>x2</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>y2</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>r2</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>x3</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>y3</value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value>r3</value>
      </testinput>
      <expected>
        <name>prtC1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtC1-2-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtC2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtC2-2-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtC3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtC3-2-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtC4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtC4-2-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR3-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR4-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(x1+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans10</name>
        <value>ev(x4+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans11</name>
        <value>y4</value>
      </testinput>
      <testinput>
        <name>ans12</name>
        <value>ev(r4+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>y1</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ev(r1+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ev(x2+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>y2</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>ev(r2+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>ev(x3+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>y3</value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value>ev(r3+1,simp)</value>
      </testinput>
      <expected>
        <name>prtC1</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC1-3-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtC2</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC2-3-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtC3</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC3-3-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtC4</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC4-3-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtR1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtR2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtR2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtR3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtR3-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtR4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtR4-1-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>x1</value>
      </testinput>
      <testinput>
        <name>ans10</name>
        <value>x4</value>
      </testinput>
      <testinput>
        <name>ans11</name>
        <value>ev(y4+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans12</name>
        <value>r4</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ev(y1+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>r1</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>x2</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>ev(y2+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>r2</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>x3</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>ev(y3+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value>r3</value>
      </testinput>
      <expected>
        <name>prtC1</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC1-2-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtC2</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC2-2-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtC3</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC3-2-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtC4</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC4-2-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtR1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR3-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR4-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(x1+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans10</name>
        <value>ev(x4+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans11</name>
        <value>ev(y4+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans12</name>
        <value>r4</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ev(y1+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>r1</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ev(x2+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>ev(y2+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>r2</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>ev(x3+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>ev(y3+1,simp)</value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value>r3</value>
      </testinput>
      <expected>
        <name>prtC1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC1-3-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtC2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC2-3-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtC3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC3-3-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtC4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prtC4-3-F</expectedanswernote>
      </expected>
      <expected>
        <name>prtR1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR3-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prtR4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prtR4-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
