Question

please help solve. find the center and radius of the circle. x^2 + y^2 - 10x - 16y + 80 = 0 please show steps

Answer 1

put x terms together
put y terms together
complete teh square for each

Answer 2

x^2 + y^2 - 10x - 16y + 80 = 0

x^2 - 10x + y^2 - 16y = -80

Answer 3

familiear with completing the square ?

Answer 4

im not that great at it

Answer 5

give it a try

Answer 6

x^2 - 10x

take half of 10, you get 5. square it and add both sides

Answer 7

do the same for y^2 - 16y

Answer 8

x^2 + y^2 - 10x - 16y + 80 = 0

x^2 - 10x + y^2 - 16y = -80

x^2 - 10x + `5^2` + y^2 - 16y + `8^2` = -80 + `5^2` + `8^2`

(x-5)^2 + (y-8)^2 = -80 + 25 + 64

(x-5)^2 + (y-8)^2 = 9

Answer 9

so its not x=4+- 10^2

Answer 10

thats it! see if that makes more or less sense..

Answer 11

so the equation of circle in center radius form is :

(x-5)^2 + (y-8)^2 = 3^2

center = (5, 8)
radius = 3

Answer 12

let me knw if something doesn't make sense

Answer 13

how you get 5 for completing the square?

Answer 14

thats a very good question

Answer 15

x^2 + y^2 - 10x - 16y + 80 = 0

x^2 - 10x + y^2 - 16y = -80

x^2 - 10x + `5^2` + y^2 - 16y + `8^2` = -80 + `5^2` + `8^2`

Answer 16

you're fine till this step ?

Answer 17

ya thats where i get stuck i can get everything past that part

Answer 18

you're fine with 3rd line, right ?

Answer 19

x^2 + y^2 - 10x - 16y + 80 = 0

x^2 - 10x + y^2 - 16y = -80

x^2 - 10x + `5^2` + y^2 - 16y + `8^2` = -80 + `5^2` + `8^2`

Answer 20

all above lines make sense ?

Answer 21

i dont get the completing the square part how you get the 5 and 8

Answer 22

x^2 - 10x

5 is half of x coefficient

Answer 23

y^2 - 16y

8 is half of y coefficient

Answer 24

its just a process, memorize it for now

Answer 25

so its just half of y?

Answer 26

its half of y coefficient

Answer 27

k i think i got it... the equation made it look like there was more to it