Find the Center and Radius (x+5)^2+(y-10)^2=9

Problem

(x+5)2+(y−10)2=9

Solution

1. Identify the standard form of a circle's equation, which is (x−h)2+(y−k)2=r2 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 and the constant as a square.

(x−(−5))2+(y−10)2=3

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

h=−5

k=10

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

r2=9

r=3

Final Answer

Center: *(−5,10), Radius: *3

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