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Identify the center and radius. (X−8)2+y2=12(X-8)^2+y^2=12

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Full solution

Q. Identify the center and radius. (X−8)2+y2=12(X-8)^2+y^2=12
  1. Recognize standard form: Recognize the standard form of a circle's equation.\newlineThe 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 and rr is the radius.
  2. Compare with standard form: Compare the given equation with the standard form.\newlineGiven equation: (X−8)2+y2=12(X-8)^2+y^2=12\newlineStandard form: (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2
  3. Identify center: Identify the center (h,k)(h,k) from the given equation.\newlineCenter (h,k)=(8,0)(h,k) = (8,0) because (X−8)(X-8) corresponds to (x−h)(x-h) and yy corresponds to (y−k)(y-k).
  4. Find radius: Find the radius by taking the square root of the right side of the equation.\newlineRadius r=12=23r = \sqrt{12} = 2\sqrt{3}

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