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Determine the center and radius of the circle represented by the equation (x+20)2+(y−30)2=225(x+20)^2+(y-30)^2=225

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Full solution

Q. Determine the center and radius of the circle represented by the equation (x+20)2+(y−30)2=225(x+20)^2+(y-30)^2=225
  1. Identify Circle Equation Form: The given equation is in the 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 of the circle and rr is the radius.
  2. Find Center Coordinates: To find the center (h,k)(h, k), we compare the given equation (x+20)2+(y−30)2=225(x+20)^2+(y-30)^2=225 with the standard form. We see that h=−20h = -20 and k=30k = 30.
  3. Calculate Radius: To find the radius rr, we take the square root of the right side of the equation. The square root of 225225 is 1515, so r=15r = 15.
  4. Final Solution: We have found the center to be (−20,30)(-20, 30) and the radius to be 1515. This completes the solution.

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