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Identify the center and radius. (x-6)^(2)+(y-1)^(2)=9

Identify the center and radius.\newline (x−6)2+(y−1)2=9 (x-6)^{2}+(y-1)^{2}=9

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Full solution

Q. Identify the center and radius.\newline (x−6)2+(y−1)2=9 (x-6)^{2}+(y-1)^{2}=9
  1. Recognize standard form: Recognize the standard form of a circle's equation, which 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 given equation: Compare the given equation x−6)2+(y−1)2=9 withthestandardform.Identify$h=6x-6)^2 + (y-1)^2 = 9\ with the standard form. Identify \$h=6, k=1k=1, and r2=9r^2=9.
  3. Calculate radius: Calculate the radius rr by taking the square root of 99. r=9=3r = \sqrt{9} = 3.

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