Find the Center and Radius y^2+4x-20-2y=-x^2

Problem

y2+4*x−20−2*y=−x2

Solution

1. Rearrange the equation into the standard form of a circle by moving all variables to the left side and the constant to the right side.

x2+4*x+y2−2*y=20

2. Group the x terms and y terms together to prepare for completing the square.

(x2+4*x)+(y2−2*y)=20

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

(x2+4*x+4)+(y2−2*y+1)=20+4+1

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

(x+2)2+(y−1)2=25

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

h=−2

k=1

r2=25⇒r=5

Final Answer

Center: *(−2,1), Radius: *5

Want more problems? Check here!