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<font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Determina la ecuación de la circunferencia que muestra la figura:<br /><br style="font-family: times new roman,times,serif;" /></span></font> <div style="text-align: center;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">#c1</span></font><br /><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;"></span></font></div>
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<font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Solución:</span><br style="font-family: times new roman,times,serif;" /><br style="font-family: times new roman,times,serif;" /><span style="font-family: times new roman,times,serif;">La ecuación general de la circunferencia es de la forma:</span><br style="font-family: times new roman,times,serif;" /><br style="font-family: times new roman,times,serif;" /></font> <div style="text-align: center;"><font size="4" style="font-style: italic;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»h«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mfenced»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»k«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/math»</span><br style="font-family: times new roman,times,serif;" /></font> <div style="text-align: left;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Donde </span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfenced»«mrow»«mi»h«/mi»«mo»,«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math»</span><span style="font-family: times new roman,times,serif;"> es el centro y </span>"<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»r«/mi»«/math»</span>"<span style="font-family: times new roman,times,serif;"> es el radio.</span></font><br /><br /><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Según nuestro gráfico, podemos observar que el centro es el punto </span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#P1«/mi»«/math»</span><span style="font-family: times new roman,times,serif;"> y </span><span style="font-family: times new roman,times,serif;">el radio es </span></font><font size="4" style="font-style: italic;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#r«/mi»«/math»</span></font><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;"> unidades.</span></font><br /><br /><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Reemplazando el centro y el radio en la circunferencia, obtenemos:<br /><br /></span></font> <div style="text-align: center;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mtable»«mtr»«mtd»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»#h1«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mfenced»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»#k1«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«msup»«mi»#r«/mi»«mn»2«/mn»«/msup»«/mtd»«/mtr»«/mtable»«/math»</span></span></font><br /> <div style="text-align: left; font-family: times new roman,times,serif; font-style: italic;"><font size="4">Por lo tanto, la ecuación de la circunferencia es:<br /><br /></font> <div style="text-align: center;"><font size="4"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mtable»«mtr»«mtd»«msup»«mfenced»«mrow»«mi»x«/mi»«mi»#c2«/mi»«mi»#h2«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mfenced»«mrow»«mi»y«/mi»«mi»#c3«/mi»«mi»#k2«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«msup»«mi»#r«/mi»«mn»2«/mn»«/msup»«/mtd»«/mtr»«/mtable»«/math»</span><br /></font></div></div> <div style="text-align: left;"><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Desarrollando la ecuación anterior, obtenemos la siguiente ecuación equivalente.</span><br style="font-family: times new roman,times,serif;" /><br style="font-family: times new roman,times,serif;" /></font> <div style="text-align: center;"><font size="4" style="font-style: italic;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mi»#c4«/mi»«mi»#A«/mi»«mi»#x«/mi»«mi»#c5«/mi»«mi»#B«/mi»«mi»#y«/mi»«mi»#c6«/mi»«mi»#C«/mi»«mo»=«/mo»«mn»0«/mn»«/math»</span></font><br /></div></div><span style="font-style: italic;"><font size="4"><span style="font-family: times new roman,times,serif;"></span></font></span><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;"></span></font></div></div></div>
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Algorithm
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<font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">Bien. Continúa de esta manera.</span></font>
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#n1
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<font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">Recuerda que en la ecuación general de la circunsferencia, el radio es al cuadrado.</span></font>
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#n2
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<font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Revisa los signos del centro al reemplazarlos en la ecuación.</span></font>
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#n3
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<font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">Revisa los signos del centro cuando los reemplaces en la ecuación y también que en la ecuación general de la circunferencia el radio sea al cuadrado.</span></font>
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Tuesday, 17 September 2013, 9:51 AM
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Tuesday, 17 September 2013, 9:51 AM
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