Find the Center and Radius x^2+y^2+4x-7=0

Problem

x^2+y^2+4*x−7=0

Solution

1. Group the x terms together and move the constant term to the right side of the equation.

x^2+4*x+y^2=7

2. Complete the square for the x terms by taking half of the coefficient of x which is 2 squaring it to get 4 and adding it to both sides.

x^2+4*x+4+y^2=7+4

3. Rewrite the x quadratic as a perfect square and simplify the right side.

(x+2)^2+y^2=11

4. Compare the equation to the standard form of a circle (x−h)^2+(y−k)^2=r^2 to identify the center (h,k) and the radius r

h=−2

k=0

r^2=11

5. Solve for the radius by taking the square root of 11

r=√(,11)

Final Answer

Center: *(−2,0), Radius: √(,11)

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