Find the Center and Radius x^2+y^2+8x-6y-24=0

Problem

x^2+y^2+8*x−6*y−24=0

Solution

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

x^2+8*x+y^2−6*y=24

2. Complete the square for the x terms by adding (8/2)^2=16 to both sides.

x^2+8*x+16+y^2−6*y=24+16

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

x^2+8*x+16+y^2−6*y+9=24+16+9

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

(x+4)^2+(y−3)^2=49

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

h=−4

k=3

r^2=49⇒r=7

Final Answer

Center: *(−4,3), Radius: *7

Want more problems? Check here!