Question

just started this unit kind of confused
what is the radius of a circle with the equation x^2+y^2+6x-2y+3=0??

Answer 1

you need to use complete the squares. Do you know how to do that?

Answer 2

i do not

Answer 3

ok so you know how (x-1)^2 for instance equals x^2-2x+1

Answer 4

uh huh

Answer 5

so we are going to need to work backwards from what i just showed you. the first step is to re arrange the equation with all the x terms next to eachother and the y terms near eachother and the constant terms on the other side.

it will look like this x^2+6x+y^2-2y=-3

make sense so far?

Answer 6

yes

Answer 7

now here is something you have to memorize. this method only works when you have x^2 and not like 3x^2. you take the term next to the x in our case we have 6x so we take 6 and divide it by 2 to get 3 then we square it and get 9 which we will add to both sides you will have to do the same thing for y as well. See if you are able to do that.

Answer 8

im not sure how to do the beginning but is it =6?

Answer 9

if you add 9 to both sides you will get =6 but you will need to also need to complete the square for y take -2 divite by 2 which equals -1 and then square which equals 1

you would get x^2+6x+9+y^2-2y+1=-3+9+1 do you see why?

Answer 10

yeah sort of

Answer 11

ok well maybe this will help clear it up for you. You may be asking why did we have to do all that work in the first place. well if you notice

x^2+6x+9 = (x+3)^2

and

y^2-2y+1 = (y-1)^2

verify this for yourself please.

so we can rewirte this equation as

(x+3)^2+(y-1)^2=7