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

The equation of a circle is (x−1)2+(y−2)2=36 (x-1)^{2}+(y-2)^{2}=36 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (1,2) (1,2) and the radius is 66 .\newlineB The center is (1,−2) (1,-2) and the radius is 66 .\newline(C) The center is (−1,2) (-1,2) and the radius is 66 .\newlineD The center is (1,2) (1,2) and the radius is 3636 .

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Full solution

Q. The equation of a circle is (x−1)2+(y−2)2=36 (x-1)^{2}+(y-2)^{2}=36 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (1,2) (1,2) and the radius is 66 .\newlineB The center is (1,−2) (1,-2) and the radius is 66 .\newline(C) The center is (−1,2) (-1,2) and the radius is 66 .\newlineD The center is (1,2) (1,2) and the radius is 3636 .
  1. Equation of a Circle: The equation of a circle in the standard form is (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where (h,k)(h, k) is the center of the circle and rr is the radius.
  2. Comparing with Standard Form: The given equation of the circle is (x−1)2+(y−2)2=36(x - 1)^2 + (y - 2)^2 = 36. By comparing this with the standard form, we can directly read off the center and the radius of the circle.
  3. Finding the Center: The center of the circle is (h,k)=(1,2)(h, k) = (1, 2) because the equation is in the form (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, and we have (x−1)2+(y−2)2=36(x - 1)^2 + (y - 2)^2 = 36.
  4. Finding the Radius: The radius of the circle is the square root of the number on the right side of the equation, which is 36\sqrt{36}. The square root of 3636 is 66.
  5. Final Answer: Therefore, the center of the circle is (1,2)(1, 2) and the radius is 66. This corresponds to answer choice (A)(A).

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