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The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation

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Answer to a math question The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation

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Frederik
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64 Answers
Para calcular la ecuación de una circunferencia, necesitamos determinar su centro y su radio.

Paso 1: Encontrar el centro de la circunferencia
El centro de una circunferencia se encuentra en el punto medio de su diámetro. En este caso, los extremos del diámetro son (-5, -4) y (3, 6).

La fórmula para encontrar el punto medio de un segmento de línea con extremos (x1, y1) y (x2, y2) es:

(\frac{x1+x2}{2}, \frac{y1+y2}{2})

Aplicando la fórmula, encontramos que el centro de la circunferencia es:

(-5, -4) + (3, 6) / 2 = (-1, 1)

Paso 2: Encontrar el radio de la circunferencia
El radio de una circunferencia se puede encontrar calculando la distancia entre cualquiera de sus extremos del diámetro y el centro. En este caso, podemos usar la fórmula de distancia entre dos puntos:

d = \sqrt{{(x2-x1)^2 + (y2-y1)^2}}

Usando los puntos (-5, -4) y (-1, 1), la distancia es:

d = \sqrt{{(-1-(-5))^2 + (1-(-4))^2}} = \sqrt{{16 + 25}} = \sqrt{{41}}

Paso 3: Escribir la ecuación de la circunferencia
La ecuación de una circunferencia con centro (h, k) y radio r es:

(x-h)^2 + (y-k)^2 = r^2

En este caso, el centro es (-1, 1) y el radio es \sqrt{{41}} :

(x-(-1))^2 + (y-1)^2 = (\sqrt{{41}})^2

Simplificando:

(x+1)^2 + (y-1)^2 = 41

¡Respuesta! La ecuación de la circunferencia es (x+1)^2 + (y-1)^2 = 41

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