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Identify the center and radius. 3. x^(2)+(y+2)^(2)=64

Identify the center and radius.\newlinex2+(y+2)2=64 x^{2}+(y+2)^{2}=64

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Full solution

Q. Identify the center and radius.\newlinex2+(y+2)2=64 x^{2}+(y+2)^{2}=64
  1. Recognize standard form: Step 11: Recognize the standard form of a circle's equation. The 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. Given equation: x2+(y+2)2=64x^2 + (y+2)^2 = 64
  2. Compare with standard form: Step 22: Compare the given equation with the standard form to find hh, kk, and rr. From x2+(y+2)2=64x^2 + (y+2)^2 = 64, we can see it matches (x−0)2+(y+2)2=64(x - 0)^2 + (y + 2)^2 = 64. Thus, h=0h = 0, k=−2k = -2.
  3. Identify radius: Step 33: Identify the radius.\newlineThe radius squared, r2r^2, is 6464.\newlineTo find rr, take the square root of 6464: r=64=8r = \sqrt{64} = 8.

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