Find the Center and Radius x^2+y^2+4x-6y-23=0

Problem

x2+y2+4*x−6*y−23=0

Solution

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

(x2+4*x)+(y2−6*y)=23

2. Complete the square for the x terms by adding (4/2)2=4 to both sides.

(x2+4*x+4)+(y2−6*y)=23+4

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

(x2+4*x+4)+(y2−6*y+9)=23+4+9

4. Factor the perfect square trinomials and simplify the right side.

(x+2)2+(y−3)2=36

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

h=−2

k=3

r=√(,36)=6

Final Answer

Center: *(−2,3), Radius: *6

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