Question

Write the equation x^2 + y^2 - 8y - 4 = -16 in standard form.

Answer 1

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:

(
`(b)/(2)`)²

In this case b is -8

`((-8)/(2) )^(2)`

(-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 (
`(b)/(2)`)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