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<font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">¿Cuál es el lugar geométrico descrito por la trayectoria de un avión que se mantiene sobrevolando sobre la ciudad de #ciudad a una distancia constante de #r km de la torre de aterrizaje? </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;">Escribe la ecuación del lugar geométrico.</span></font>
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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;">Como el avión se encuentra sobrevolando a una distancia constante de la torre de aterrizaje, podemos darnos cuenta que el lugar geométrico es una circunferencia.</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 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-family: times new roman,times,serif; font-style: italic;"><font size="4"><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 /></font> <div style="text-align: left;"><font size="4">Donde <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> es el centro y <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«/math»</span> es el radio.<br /><br /></font></div></div><font size="4" style="font-family: times new roman,times,serif; font-style: italic;">Si le asignamos el punto <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«/mrow»«/mfenced»«/math»</span> a la torre de aterrizaje, entonces el centro de la circunferencia es <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«/mrow»«/mfenced»«/math»</span> y el radio es <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#r«/mi»«/math»</span></font><font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">.</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;">Observemos la figura que indica que trayectoria del avión:</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 style="font-family: times new roman,times,serif;">#c1</span><br style="font-family: times new roman,times,serif;" /><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;">Reemplazando el centro y radio en la ecuación de la circunferencia, obtenemos:</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»«mn»0«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mfenced»«mrow»«mi»y«/mi»«mo»-«/mo»«mn»0«/mn»«/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;">Por lo tanto, el lugar geométrico que describe la trayectoria del avión es:</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»«mo»=«/mo»«msup»«mi»#r«/mi»«mn»2«/mn»«/msup»«/math»</span></font><br /></div></div></div></div></div>
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<font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">¡Excelente!</span></font>
Answer 2
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<font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">¡Excelente!</span></font>
Answer 3
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Answer 4
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None
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33.33333%
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14.28571%
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33.33333%
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