A circle in the xy-plane has the equation (x+17.5)^(2)+(y-15. bar(3))^(2)=18.1 Which of the following best describes the location of the center of the circle and the length of its radius? Choose 1 answer: (A) Center: (-17.5,15. bar(3)) Radius: sqrt18.1 (B) Center: (-17.5,15. bar(3)) Radius: 18.1 (C) Center: (17.5,-15. bar(3)) Radius: sqrt18.1 (D) Center: (17.5,-15. bar(3)) Radius: 18.1

Question

A circle in the  xy-plane has the equation  (x+17.5)^(2)+(y-15. bar(3))^(2)=18.1 Which of the following best describes the location of the center of the circle and the length of its radius? Choose 1 answer: (A) Center:  (-17.5,15. bar(3)) Radius:  sqrt18.1 (B) Center:  (-17.5,15. bar(3)) Radius: 18.1 (C) Center:  (17.5,-15. bar(3)) Radius:  sqrt18.1 (D) Center:  (17.5,-15. bar(3)) Radius: 18.1

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Identifying the Center: The equation of a circle in the xy-plane is given by the formula $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. We need to compare this formula with the given equation $(x+17.5)^2 + (y-15.\overline{3})^2 = 18.1$ to find the center and the radius of the circle.Determining the Radius: First, we identify the center of the circle by looking at the terms $(x+17.5)^2$ and $(y-15.\overline{3})^2$. According to the standard form of the circle's equation, the center $(h, k)$ will be the opposite signs of the values inside the parentheses. Therefore, the center is $(-17.5, 15.\overline{3})$.Comparing with Answer Choices: Next, we determine the radius of the circle. The radius squared $r^2$ is equal to the constant term on the right side of the equation, which is $18.1$. To find the radius $r$, we take the square root of $18.1$, which is $\sqrt{18.1}$.Now we can compare our findings with the given answer choices. The center we found is $(-17.5, 15.\overline{3})$ and the radius is $\sqrt{18.1}$. This matches with option (A).

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