Find the Center and Radius (x+3)^2+(y-2)^2=4

Problem

(x+3)^2+(y−2)^2=4

Solution

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

2. Rewrite the given equation to match the standard form by expressing the addition as subtraction of a negative number.

(x−(−3))^2+(y−2)^2=2^2

3. Extract the coordinates of the center (h,k) from the rewritten equation.

h=−3

k=2

4. Determine the radius r by taking the square root of the constant on the right side of the equation.

r^2=4

r=√(,4)

r=2

Final Answer

Center: *(−3,2), Radius: *2

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