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Find the center and radius of the circle (x-2)^(2)+(y+1)^(2)=36 Solution The center of the circle is at: C=(2,-1). The radius of the circle is r=6. Explanation A circle with center at (h,k) and a radius of r has equation (x-h)^(2)+(y-k)^(2)=r^(2). In this example our circle equation can be written as: (x-2)^(2)+(x-(-1))^(2)=(h)^(2)

Find the center and radius of the circle (x−2)2+(y+1)2=36 (x-2)^{2}+(y+1)^{2}=36 \newlineSolution\newlineThe center of the circle is at: C=(2,−1) C=(2,-1) .\newlineThe radius of the circle is r=6 r=6 .\newlineExplanation\newlineA circle with center at (h,k) (h, k) and a radius of r r has equation (x−h)2+(y−k)2=r2 (x-h)^{2}+(y-k)^{2}=r^{2} .\newlineIn this example our circle equation can be written as:\newline(x−2)2+(x−(−1))2=(h)2 (x-2)^{2}+(x-(-1))^{2}=(h)^{2}

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Q. Find the center and radius of the circle (x−2)2+(y+1)2=36 (x-2)^{2}+(y+1)^{2}=36 \newlineSolution\newlineThe center of the circle is at: C=(2,−1) C=(2,-1) .\newlineThe radius of the circle is r=6 r=6 .\newlineExplanation\newlineA circle with center at (h,k) (h, k) and a radius of r r has equation (x−h)2+(y−k)2=r2 (x-h)^{2}+(y-k)^{2}=r^{2} .\newlineIn this example our circle equation can be written as:\newline(x−2)2+(x−(−1))2=(h)2 (x-2)^{2}+(x-(-1))^{2}=(h)^{2}
  1. Identify Form & Compare: Identify the general form of the circle's equation and compare it with the given equation to find the center and radius.
  2. Calculate Radius: Calculate the radius from the value of r2r^2.
  3. Write Center & Radius: Write down the center and radius of the circle.

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