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

Problem

4*x2+4*y2+4*x+4*y−2=0

Solution

1. Divide the entire equation by 4 to make the coefficients of x2 and y2 equal to 1

x2+y2+x+y−1/2=0

2. Rearrange the equation by grouping the x terms and y terms together and moving the constant to the other side.

(x2+x)+(y2+y)=1/2

3. Complete the square for both the x and y expressions by adding (1/2)2=1/4 to both groups and the right side of the equation.

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

4. Simplify the right side and write the left side as squared binomials.

(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!