Question

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.

x^2 − 4x + y^2 + 8y = −4

Answer 1

Use mathway

Answer 2

...

Answer 3

ever heard of pemdas

Answer 4

Soup its the circle equation thing its not just regular pemdas

Answer 5

circle thing?

Answer 6

do you mean graphing

Answer 7

no like i have to find the center point of the circle and the radius, there is also a certain formula it has to be set up in. Its the circle formula thingy.

Answer 8

remember that a perfect square trinomial takes the form

a^2 + 2ab + b^2 = (a+b)^2

you want to re-write the x and y terms to make a perfect square. you can do this by adding terms to each side of the equation.

x^2 − 4x + y^2 + 8y = −4

let's just look at the x terms

x^2 - 4x

to get the last term in our perfect square, we take the coefficient of x, divide by 2, square it, and add it to both sides of the equation. in this case, our coefficient of x is -4 (notice -4x), we divide this by 2 to get -2, then square this to get (-2)^2 = 4. so we can add 4 to both sides to keep both sides of the equation equal.

x^2 − 4x + 4 + y^2 + 8y = −4 + 4

why do this? we can use our perfect square trinomial formula to re-write x^2 - 4x + 4 as (x-2)^2

giving us:

(x-2)^2 + y^2 + 8y = 0

repeat this process with the y terms. when done properly, you'll have an equation in the form (x-h)^2 + (y-k)^2 = r^2 which will let you identify your center (h,k) and your radius r.