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The equation of a circle is (x+2)^(2)+(y+6)^(2)=16. What are the center and radius of the circle? Choose 1 answer: (A) The center is (2,-6) and the radius is 6 . (B) The center is (-2,6) and the radius is 6 . (C) The center is (-2,-6) and the radius is 4 . (D) The center is (1,2) and the radius is 16 .

The equation of a circle is (x+2)2+(y+6)2=16 (x+2)^{2}+(y+6)^{2}=16 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (2,−6) (2,-6) and the radius is 66 .\newline(B) The center is (−2,6) (-2,6) and the radius is 66 .\newline(C) The center is (−2,−6) (-2,-6) and the radius is 44 .\newline(D) The center is (1,2) (1,2) and the radius is 1616 .

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Q. The equation of a circle is (x+2)2+(y+6)2=16 (x+2)^{2}+(y+6)^{2}=16 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (2,−6) (2,-6) and the radius is 66 .\newline(B) The center is (−2,6) (-2,6) and the radius is 66 .\newline(C) The center is (−2,−6) (-2,-6) and the radius is 44 .\newline(D) The center is (1,2) (1,2) and the radius is 1616 .
  1. Circle Equation Standard Form: The equation of a circle in 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. Compare with Given Equation: Given the equation of the circle is (x+2)2+(y+6)2=16(x + 2)^2 + (y + 6)^2 = 16, we can compare it to the standard form to find the center and the radius.
  3. Find Center: The center of the circle is found by looking at the values that xx and yy are being added or subtracted by inside the parentheses. In the standard form, we subtract hh from xx and kk from yy. In our equation, we are adding 22 to xx and 66 to yy, which means yy00 and yy11. Therefore, the center is yy22.
  4. Find Radius: The radius of the circle is the square root of the value on the right side of the equation. Since the right side of the equation is 1616, we take the square root of 1616 to find the radius, which is 44.
  5. Match with Options: Now we can match our findings with the given options. The center is (−2,−6)(-2, -6) and the radius is 44, which corresponds to option (C)(C).

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