x² - 10x + y² + 8y = 28
Take one-half the -10, which is -5
Square -5. Get +25
Add +25 to both sides, putting it right after the -10x on the left
x² - 10x + 25 + y² + 8y = 28 + 25
Take one-half the +8, which is +4
Square +4. Get +16
Add +16 to both sides, putting it right after the 8y on the left
x² - 10x + 25 + y² + 8y + 16 = 28 + 25 + 16
Combine the terms on the right
x² - 10x + 25 + y² + 8y + 16 = 69
Factor the first three terms on the left as (x - 5)(x - 5) and
then write it as (x - 5)²
(x - 5)² + y² + 8y + 16 = 69
Factor the last three terms on the left as (y + 4)(y + 4) and
then write it as (y + 4)²
(x - 5)² + (y + 4)² = 69
Compare to
(x - h)² + (y - k)² = r²
Then
-h = -5 so h = 5
-k = +4 so k = -4
So center = (h,k) = (5,-4)
__
r² = 69, so r = Ö69
Edwin
