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The equation of a circle is (x+3)^(2)+(y-4)^(2)=49. What are the center and radius of the circle? Choose 1 answer: (A) The center is (3,4) and the radius is 7 . (B) The center is (-3,4) and the radius is 7 . (c) The center is (-3,-4) and the radius is 7 . (D) The center is (-3,4) and the radius is 49 .

The equation of a circle is (x+3)2+(y−4)2=49 (x+3)^{2}+(y-4)^{2}=49 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (3,4) (3,4) and the radius is 77 .\newline(B) The center is (−3,4) (-3,4) and the radius is 77 .\newline(C) The center is (−3,−4) (-3,-4) and the radius is 77 .\newline(D) The center is (−3,4) (-3,4) and the radius is 4949 .

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Full solution

Q. The equation of a circle is (x+3)2+(y−4)2=49 (x+3)^{2}+(y-4)^{2}=49 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (3,4) (3,4) and the radius is 77 .\newline(B) The center is (−3,4) (-3,4) and the radius is 77 .\newline(C) The center is (−3,−4) (-3,-4) and the radius is 77 .\newline(D) The center is (−3,4) (-3,4) and the radius is 4949 .
  1. Equation of a Circle: 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. We need to compare the given equation (x+3)2+(y−4)2=49(x+3)^2 + (y-4)^2 = 49 with the standard form to find the center and the radius.
  2. Finding the Center: The given equation is already in standard form. To find the center (h,k)(h, k), we look at the signs in front of the numbers inside the parentheses. The center will be (−3,4)(-3, 4) because the equation has (x+3)(x+3) and (y−4)(y-4), which means h=−3h = -3 and k=4k = 4.
  3. Finding the Radius: To find the radius rr, we take the square root of the number on the right side of the equation. The square root of 4949 is 77, so the radius of the circle is 77.
  4. Matching the Information: Now we have the center (−3,4)(-3, 4) and the radius 77. We can match this information with the answer choices.

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