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(x-17)^(2)+(y-19)^(2)=49 A circle in the xy-plane has the equation shown. How long is the radius of the circle?

(x−17)2+(y−19)2=49 (x-17)^{2}+(y-19)^{2}=49 \newlineA circle in the xy x y -plane has the equation shown. How long is the radius of the circle?

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Full solution

Q. (x−17)2+(y−19)2=49 (x-17)^{2}+(y-19)^{2}=49 \newlineA circle in the xy x y -plane has the equation shown. How long is the radius of the circle?
  1. Identify Circle Equation: The equation of a circle in the xy-plane is given by (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 radius, we need to compare the given equation with the standard form.
  2. Compare with Standard Form: The given equation is x-17)^2 + (y-19)^2 = 49\. By comparing this with the standard form, we can see that the right side of the equation, \$49, represents r2r^2, the square of the radius.
  3. Calculate Square Root: To find the radius rr, we take the square root of 4949. The square root of 4949 is 77.
  4. Find Radius: Therefore, the radius of the circle is 77 units.

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