Find the Center and Radius (x+4)^2+(y-1)^2=9

Problem

(x+4)2+(y−1)2=9

Solution

1. Identify the standard form of a circle equation, which is (x−h)2+(y−k)2=r2 where (h,k) represents the center and r represents the radius.

2. Determine the center by comparing the given equation (x+4)2+(y−1)2=9 to the standard form. Since x+4 is equivalent to x−(−4) we find h=−4 and k=1

3. Determine the radius by setting r2 equal to the constant on the right side of the equation.

r2=9

4. Solve for r by taking the square root of both sides.

r=√(,9)

r=3

Final Answer

Center: *(−4,1), Radius: *3

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