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(x+55)^(2)+(y-11.5)^(2)=121 A circle in the xy-plane has the equation shown. What is the length of the diameter of the circle?

(x+55)2+(y−11.5)2=121 (x+55)^{2}+(y-11.5)^{2}=121 \newlineA circle in the xy x y -plane has the equation shown. What is the length of the diameter of the circle?

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Find properties of circles from equations in general formright chevron icon

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Q. (x+55)2+(y−11.5)2=121 (x+55)^{2}+(y-11.5)^{2}=121 \newlineA circle in the xy x y -plane has the equation shown. What is the length of the diameter of the circle?
  1. Identify Circle Standard Equation: The given equation is in the form of a circle's standard 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 of the circle and rr is the radius of the circle. To find the diameter, we need to identify the radius from the equation.
  2. Compare Given Equation: The given equation is x+55)\^2 + \$y-11.5)\^2 = 121. Comparing this with the standard form, we can see that the radius squared, \$r^2, is equal to 121{121}.
  3. Find Radius: To find the radius rr, we take the square root of 121121. The square root of 121121 is 1111.
  4. Calculate Diameter: The diameter of a circle is twice the radius. Therefore, the diameter DD is 22 times 1111, which is D=2×11D = 2 \times 11.
  5. Calculate Diameter: The diameter of a circle is twice the radius. Therefore, the diameter DD is 22 times 1111, which is D=2×11D = 2 \times 11.Calculating the diameter, we get D=2×11=22D = 2 \times 11 = 22.

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