Find the Center and Radius x^2+y^2+6x-6y-46=0

Problem

x2+y2+6*x−6*y−46=0

Solution

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

x2+6*x+y2−6*y=46

2. Complete the square for the x terms by adding (6/2)2=9 and for the y terms by adding ((−6)/2)2=9 to both sides.

(x2+6*x+9)+(y2−6*y+9)=46+9+9

3. Factor the perfect square trinomials into squared binomials and simplify the right side.

(x+3)2+(y−3)2=64

4. Identify the center (h,k) and the radius r by comparing the equation to the standard form (x−h)2+(y−k)2=r2

h=−3

k=3

r2=64⇒r=8

Final Answer

Center: *(−3,3), Radius: *8

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