The equation of a circle is (x-2)^(2)+(y+4)^(2)=36. What are the center and radius of the circle? Choose 1 answer: (A) The center is (2,4) and the radius is 6 . (B) The center is (2,-4) and the radius is 6 . (C) The center is (-2,-4) and the radius is 6 . (D) The center is (2,-4) and the radius is 36 .

Equation of a Circle: The equation of a circle in standard form is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.Given Equation in Standard Form: Given the equation (x - 2)² + (y + 4)² = 36, we can see that it is already in standard form. Therefore, we can directly read off the center and the radius from the equation.Center of the Circle: The center of the circle is given by (h, k). In our equation, h = 2 and k = -4, so the center is (2, -4).Radius of the Circle: The radius of the circle is given by the square root of the number on the right side of the equation. In our equation, the number is 36, so the radius r is √36, which is 6.Matching with Answer Choices: We can now match our findings with the given answer choices. The center is (2, -4) and the radius is 6, which corresponds to answer choice (B).

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The equation of a circle is
(x-2)^(2)+(y+4)^(2)=36. What are the center and radius of the circle?
Choose 1 answer:
(A) The center is
(2,4) and the radius is 6 .
(B) The center is
(2,-4) and the radius is 6 .
(C) The center is
(-2,-4) and the radius is 6 .
(D) The center is
(2,-4) and the radius is 36 .

The equation of a circle is $(x-2)^{2}+(y+4)^{2}=36$ . What are the center and radius of the circle? $\newline$ Choose $1$ answer: $\newline$ (A) The center is $(2,4)$ and the radius is $6$ . $\newline$ (B) The center is $(2,-4)$ and the radius is $6$ . $\newline$ (C) The center is $(-2,-4)$ and the radius is $6$ . $\newline$ (D) The center is $(2,-4)$ and the radius is $36$ .

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Algebra 1

Solve a system of equations using any method: word problems

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Q. The equation of a circle is

(x-2)^{2}+(y+4)^{2}=36

. What are the center and radius of the circle?

\newline

Choose

1

answer:

\newline

(A) The center is

(2,4)

and the radius is

6

\newline

(B) The center is

(2,-4)

and the radius is

6

\newline

(-2,-4)

and the radius is

6

\newline

(D) The center is

(2,-4)

and the radius is

36

Equation of a Circle: The equation of a circle in standard form is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is the radius.
Given Equation in Standard Form: Given the equation $(x - 2)^2 + (y + 4)^2 = 36$ , we can see that it is already in standard form. Therefore, we can directly read off the center and the radius from the equation.
Center of the Circle: The center of the circle is given by $(h, k)$ . In our equation, $h = 2$ and $k = -4$ , so the center is $(2, -4)$ .
Radius of the Circle: The radius of the circle is given by the square root of the number on the right side of the equation. In our equation, the number is $36$ , so the radius $r$ is $\sqrt{36}$ , which is $6$ .
Matching with Answer Choices: We can now match our findings with the given answer choices. The center is $(2, -4)$ and the radius is $6$ , which corresponds to answer choice $(B)$ .