[tex] {x}^{2} - 10x + {y}^{2} - 2y + 10 = 0[/tex]
minus 10
so it'll be
[tex] {x}^{2} - 10x + {y}^{2} - 2y = - 10[/tex]
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
[tex] {x}^{2} - 10x + (blank)[/tex]
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
[tex] {x}^{2} - 10x + 25[/tex]
now we'll do the y's
[tex] {y}^{2} - 2y + (blank)[/tex]
so take the b
which is -2
1/2(b) = -1
then (1/2(b))^2 = 1
[tex] {y}^{2} - 2y + 1[/tex]
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
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
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
[tex] {x - ( - 5)}^{2} + {y - ( - 1)}^{2} = 16 [/tex]
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
