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Find the radius of the circle. x2+y2=36x^{2}+y^{2}=36

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Full solution

Q. Find the radius of the circle. x2+y2=36x^{2}+y^{2}=36
  1. Circle Standard Form: The equation of a circle in 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. The given equation is already in standard form with h=0h = 0 and k=0k = 0, which means the center is at the origin (0,0)(0,0).
  2. Identify Radius: To find the radius, we compare the given equation x2+y2=36x^2 + y^2 = 36 to the standard form equation and identify the value of r2r^2. In this case, r2=36r^2 = 36.
  3. Calculate Radius: To find the radius rr, we take the square root of both sides of the equation r2=36r^2 = 36. The square root of 3636 is 66, so r=6r = 6.

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