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A circle in the XY-plane has the equation (x−0.8)2+(y−5.2)2=1.69(x-0.8)^2 + (y-5.2)^2=1.69. How long is the radius of the circle?

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Convert equations of circles from general to standard formright chevron icon

Full solution

Q. A circle in the XY-plane has the equation (x−0.8)2+(y−5.2)2=1.69(x-0.8)^2 + (y-5.2)^2=1.69. How long is the radius of the circle?
  1. Identify Standard Form: The equation of a circle in 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 of the circle and rr is the radius. In the given equation (x−0.8)2+(y−5.2)2=1.69(x-0.8)^2 + (y-5.2)^2=1.69, we can see that it is already in standard form with h=0.8h = 0.8, k=5.2k = 5.2, and r2=1.69r^2 = 1.69. To find the radius rr, we need to take the square root of r2r^2.
  2. Calculate Radius: Calculate the square root of 1.691.69 to find the radius rr. \newliner=1.69r = \sqrt{1.69}\newliner≈1.3r \approx 1.3
  3. Verify Calculation: Check the calculation to ensure there are no math errors. 1.69≈1.3\sqrt{1.69} \approx 1.3 is correct because 1.3×1.3=1.691.3 \times 1.3 = 1.69.

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