X^2+y^2-10x-2y+10=0 what is the center and the radius of the circle? show the work.

minus 10

so it'll be

then you want to do x^2 + 4x + (blank)+ y^2 - 6y + (blank) = -10 + (blank) + (blank)

sinnce everything is legal on math as long as you do it to both sides you want to put empty boxes which will come to usage soon

then we'll focus on the x part first so

a +b + c
so you'll take the b
which is -10
1/2(b) = -5
then do (1/2(b))^2 which will be 25

so the x portion will be

now we'll do the y's

so take the b
which is -2
1/2(b) = -1
then (1/2(b))^2 = 1

and then the numbers you just added, add to the other side of the equal sign

x^2 - 10x + 25 + y^2 - 2y + 1 = -10 + 25 + 1

then you want to factor them and add like terms

so (x - 5)^2 + (y - 1)^2 = 16

the formula for the circle is


so
center: (5, 1)
it's not negative since you're plugging in -5, and -1 into the -h and -k already
making it positive
so the formula would be with the numbers

and the radius is 4 since you have to square root the 16 to find the square of it which is 4

so it'll be

center: (5, 1)
radius: 4