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Determine the center and radius of the circle represented by the equation \newline(x−17)2+(y−19)2=49(x-17)^2+(y-19)^2=49

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Full solution

Q. Determine the center and radius of the circle represented by the equation \newline(x−17)2+(y−19)2=49(x-17)^2+(y-19)^2=49
  1. Circle Equation Form: The given equation (x−17)2+(y−19)2=49(x-17)^2+(y-19)^2=49 is in the form of a circle equation, which is generally written as (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. Identify Center: To identify the center (h,k)(h,k) of the circle, we look at the terms (x−17)(x-17) and (y−19)(y-19). The center of the circle is at (h,k)=(17,19)(h,k) = (17, 19).
  3. Find Radius: To find the radius rr of the circle, we take the square root of the right side of the equation. Since 4949 is a perfect square, r=49=7r = \sqrt{49} = 7.
  4. Circle Parameters: Now we have the center (17,19)(17, 19) and the radius 77 of the circle. The equation (x−17)2+(y−19)2=49(x-17)^2+(y-19)^2=49 represents a circle with these parameters.

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