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The equation of a circle is (x+6)^(2)+(y+8)^(2)=1. What are the center and radius of the circle? Choose 1 answer: (A) The center is (6,-8) and the radius is 1 . (B) The center is (-6,8) and the radius is 1 . (c) The center is (-6,-8) and the radius is 1 . (D) The center is (6,8) and the radius is 1 .

The equation of a circle is (x+6)2+(y+8)2=1 (x+6)^{2}+(y+8)^{2}=1 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (6,−8) (6,-8) and the radius is 11 .\newline(B) The center is (−6,8) (-6,8) and the radius is 11 .\newline(C) The center is (−6,−8) (-6,-8) and the radius is 11 .\newlineD The center is (6,8) (6,8) and the radius is 11 .

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Q. The equation of a circle is (x+6)2+(y+8)2=1 (x+6)^{2}+(y+8)^{2}=1 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (6,−8) (6,-8) and the radius is 11 .\newline(B) The center is (−6,8) (-6,8) and the radius is 11 .\newline(C) The center is (−6,−8) (-6,-8) and the radius is 11 .\newlineD The center is (6,8) (6,8) and the radius is 11 .
  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. Matching the Standard Form: The given equation is (x+6)2+(y+8)2=1(x + 6)^2 + (y + 8)^2 = 1. To match the standard form, we can see that h=−6h = -6 and k=−8k = -8, since the standard form has (x−h)(x - h) and (y−k)(y - k).
  3. Finding the Radius: The radius rr is the square root of the right side of the equation. Since the right side of the equation is 11, the radius rr is 1\sqrt{1}, which is 11.
  4. Center and Radius: Therefore, the center of the circle is (−6,−8)(-6, -8) and the radius is 11. This corresponds to choice (C)(C).

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