Question

..

Answer 1

do you know how to "complete the square" for
y^2 -2y ?

Answer 2

people often "move" the constant (the -11 ) to the other side.
add +11 to both sides
x^2 + y^2 -2y - 11 + 11= 0+11
simplify to
x^2 + y^2 -2y = 11

Answer 3

the idea is to add a number to the left side so that
y^2 -2y + k^2 is a perfect square and can be re-written as (y-k)^2

Answer 4

even if you don't know how to "complete the square" you can make a good guess.

what did they add to the right side to change
x^2 + y^2 -2y = 11

to
x^2 + (y-k)^2 = 12
?
you have to guess they added that same number to the left side to keep the equation true.

Answer 5

yes. so let's do that to both sides

x^2 + y^2 -2y +1 = 11+1
x^2 + y^2 -2y +1 = 12

now can you factor y^2 -2y+1 ?

Answer 6

to factor look at the last number +1
list all pairs of numbers that multiply to give it
+1,+1
or
-1,-1

now add the pairs.
pick the pair that adds up to the middle number -2 (from -2x)

Answer 7

your factors will by -1 and -1 which means
(y-1)(y-1)

Answer 8

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