Question

[Algebra] Find the center and radius of the circle with equation x2 y2 -2x4y 113 op

Answer 1

x^2 - 2x + y^2+ 4y = 11
(x -1)^2 + (y+2)^2 -1 - 4 = 11
(x-1)^2 + (y+2)^2 = 4^2
Center(1,-2) and radius = 4

Answer 2

what you do is get into the form
(x-h)^2+(y-k)^2=r^2
(h,k) is center
r=radis

complete the square with x and y

x^2+y^2-2x+4y-11=0
group x and y terms together
(x^2-2x)+(y^2+4y)-11=0

take 1/2 of linear coefieicnt and add postive and negative
for x^2-2x, -2/2=-1, (-1)^2=1
for y^2+4y, 4/2=2, 2^2=4

(x^2-2x+1-1)+(y^2+4y+4-4)-11=0
complete the square
(x-1)^2-1+(y+2)^2-4-11=0
add like terms
(x-1)^2+(y+2)^2-16=0
add 16 both side
(x-1)^2+(y+2)^2=16
(x-(1))^2+(y-(-2))^2=4^2
(x-h)^2+(y-k)^2=r^2

(h,k)
(1,-2)
r=4

center is (1,-2)
radius is 4 units