Find the Center and Radius (x-4)^2+y^2=16

Problem

(x−4)2+y2=16

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. Rewrite the given equation (x−4)2+y2=16 to match the standard form more closely by expressing y2 as (y−0)2

3. Compare the terms to find the coordinates of the center.

h=4

k=0

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

r2=16

r=√(,16)

r=4

Final Answer

Center: *(4,0), Radius: *4

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