To solve this question you must complete the square:
First you must make it so all the "variables" are on one side (this would be x², y², and -8y) and the non variables on the other. This means that you must add 4 to both sides
x² + y² - 8y = -12
Now you must complete the square
x² + (y² - 8y + ___) = -12 + ___
To find the blank spot you must do:
([tex]\frac{b}{2}[/tex])²
In this case b is -8
[tex](\frac{-8}{2} )^{2}[/tex]
(-4)²
16
The 16 will go in the blank parts
x² + (y² - 8y + 16) = -12 + 16
x² + (y² - 8y + 16) = 4
Now you must factor y² - 8y + 16. There is a trick to doing this. Instead of spending time looking for factors you can simply look at ([tex]\frac{b}{2}[/tex])². Your factor will be b ÷ 2. In this case that is -4
C. x² + (y - 4)² = 4
Hope this helped!
~Just a girl in love with Shawn Mendes
