Find the Center and Radius x^2+y^2+x+y-1/2=0

Problem

x2+y2+x+y−1/2=0

Solution

1. Group the terms by variable and move the constant term to the right side of the equation.

x2+x+y2+y=1/2

2. Complete the square for the x terms by adding (1/2)2=1/4 to both sides.

x2+x+1/4+y2+y=1/2+1/4

3. Complete the square for the y terms by adding (1/2)2=1/4 to both sides.

x2+x+1/4+y2+y+1/4=1/2+1/4+1/4

4. Factor the quadratic trinomials into perfect square binomials and simplify the right side.

(x+1/2)2+(y+1/2)2=1

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

h=−1/2

k=−1/2

r2=1⇒r=1

Final Answer

Center: *(−1/2,−1/2), Radius: *1

Want more problems? Check here!