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stellarik [79]
2 years ago
7

1.Encuentra la ecuación de la circunferencia que tiene como ecuación ordinaria (x-4)² + (y+5)²= 25 2- encuentra la ecuación gene

ral de la circunferencia que tiene como ecuación ordinaria (x+1)² + (y+9)²=49
Mathematics
1 answer:
rodikova [14]2 years ago
4 0

Responder:

1) x² + y²-8x + 10y + 16 = 0

2) x² + y² + x + 18y + 33 = 0

Explicación paso a paso:

A partir de la pregunta, debemos expresar la ecuación en la forma estándar de un círculo expresado como;

x² + y² + 2gx + 2fy + c = 0 donde;

(-g, -f) es el centro.

1) Para la ecuación (x-4) ² + (y + 5) ² = 25

Expande el paréntesis;

(x-4) ² + (y + 5) ² = 25

x²-8x + 16 + y² + 10x + 25 = 25

x²-8x + 16 + y² + 10y + 25-25 = 0

Recopile términos similares;

x² + y²-8x + 10y + 16 + 0 = 0

<em>x² + y²-8x + 10y + 16 = 0 </em>

<em>Por lo tanto, la ecuación requerida es x² + y²-8x + 10y + 16 = 0 </em>

<em> </em>

2) Para la expresión (x + 1) ² + (y + 9) ² = 49

x² + x + 1 + y² + 18y + 81 = 49

x² + x + 1 + y² + 18y + 81-49 = 0

Recopile términos similares;

x² + y² + x + 18y + 82-49 = 0

<em>x² + y² + x + 18y + 33 = 0 </em>

<em>Por tanto, la ecuación requerida es x² + y² + x + 18y + 33 = 0</em>

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