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Identify the center and radius. 2. (x-2)^(2)+(y+3)^(2)=36

Identify the center and radius.\newline (x−2)2+(y+3)2=36 (x-2)^{2}+(y+3)^{2}=36

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Write a quadratic function from its x-intercepts and another pointright chevron icon

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Q. Identify the center and radius.\newline (x−2)2+(y+3)2=36 (x-2)^{2}+(y+3)^{2}=36
  1. Recognize standard form: Recognize the standard form of a circle's equation.\newlineThe equation (x−2)2+(y+3)2=36(x-2)^2 + (y+3)^2 = 36 is already in the standard form (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. Identify center: Identify the center (h,k)(h, k) from the equation.\newlineFrom (x−2)2+(y+3)2=36(x-2)^2 + (y+3)^2 = 36, h=2h = 2 and k=−3k = -3. So, the center is (2,−3)(2, -3).
  3. Determine radius: Determine the radius rr. The radius squared, r2r^2, is 3636. Taking the square root of both sides, r=36=6r = \sqrt{36} = 6.

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