La hipérbola se define como el lugar geométrico de los puntos del plano, cuya diferencia de distancias a dos puntos fijos es constante.[br][br]Sobre una recta dibujamos los puntos O, A y F que corresponden al centro, vértice y foco de la hipérbola. A continuación utilizando la herramienta Refleja objeto por punto obtenemos los puntos simétricos A’ y F’.[br][img width=441,height=92]data:image/png;base64,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[/img][br]A continuación, situamos un punto P sobre la recta inicial y definimos los segmentos PA y PA’.[br][br]Trazamos dos circunferencias, una con centro en el punto F y radio PA, y otra con centro en el otro foco F’ y radio PA’.[br][br]Los puntos de intersección P1 y P2 de las dos circunferencias son puntos de la hipérbola.[br][img width=384,height=295]data:image/png;base64,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hipérbola se obtiene como lugar geométrico de cada uno de los puntos anteriores, cuando el punto P recorre la recta inicial.[br][br]Utilizaremos la herramienta [b]Lugar geométrico[/b] para obtener el lugar descrito por el punto P1 cuando el punto P recorre la recta inicial y a continuación, el lugar descrito por el punto P2 cuando P se mueve por la recta.[br][br]