Determina el centro,radio y gráfica de la circunferencia:(x+2)2 + (y-3)2=121
1 answer:
Answer:
La ecuación genérica para un círculo centrado en el punto (a, b), de radio R, es:
(x - a)^2 + (x - b)^2 = R^2
Entonces si miramos a nuestra ecuación:
(x + 2)^2 + (y - 3)^2 = 121
Tendremos el centro en:
(-2, 3)
el radio está dado por:
R^2 = 121
R = √121 = 11
La gráfica de esta circunferencia se puede ver en la imagen de abajo.
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The error is when she added 4 to both sides.
Instead, she should divide both sides by -4 to undo the multiplication. Specifically, the multiplication between the -4 term and the (x-2)^2 term.
This is one possible correction of what her steps could look like.
In the third step, I'm dividing both sides by -4. In the sixth step, I'm applying the square root to both sides to undo the squaring operation. Then two steps later, I'm adding 2 to both sides to undo the "-2", which helps fully isolate x.
The only solution is x = 2, so it's the only x intercept. You can verify this answer by plugging x = 2 back into the original equation at the very top. You should end up with y = 0.
Note: The term "root" is another name for "x intercept".