Question

I need to find the center,radius, and then graph this
x^2+y^2+10y+21=0

Answer 1

I know the formula would be (x-a)^2(y-b)^2=r^2

Answer 2

Whatever you said above was correct.
(h,k) is the center of (x-h)^2 + (y-k)^2 = r^2

now when you expand all the terms,

x^2 -2xh + h^2 + y^2 - 2yk + k^2 = r^2

x^2 + y^2 -2hx -2ky + h^2 + k^2 - r^2 =0

Your given equation is of this form only.
Now recall that (h,k) was the center
that means if the expression is represented like this, then negative halves of the coefficients of x and y are the respective co-ordinates of the center of the circle.

for example,
in x^2 + y^2 - 2x + 4y + 2 = 0

(-(-2)/2 , -(4)/2 ) are the co-ordinates of the center
i.e. (1,-2) is the center
now, using this, can you tell the center of your given equation ?

Answer 3

@shubhamsrg gave you a complete explanation, you still pump it. where are you stuck?

Answer 4

make questions, one by one, please. If I can, I will explain. If I cannot, I will tag other for help.

Answer 5

Ok I am now stuck at x^2 + y^2 -2hx -2ky + h^2 + k^2 - r^2 =0

Answer 6

you don't know why you need that form, right?

Answer 7

to find the center and radius?

Answer 8

yes.

Answer 9

because that form is expanding form of (x-h)^2 +(y-k)^2 = something.

Answer 10

ok, break it down. expand this first: (x-h)^2 = ?

Answer 11

x^2-h^2

Answer 12

nope, friend, not that. again, try !! if you don't know, google. by that way, you remember your mistake.

Answer 13

I can give you, Sure!! but I want you find out by yourself

Answer 14

what do you mean expand?

Answer 15

ooooooooo

Answer 16

wait I got it

Answer 17

(x-h)(x-h)

Answer 18

(x -h)^2 = x^2 -2xh +h^2 . That's called "expand"

Answer 19

yes!! your way is ok, just one more step to get mine

Answer 20

oh well I was off

Answer 21

and now , expand (y-k)^2 = ?

Answer 22

(y-k)^2=y^2-2yk+h^2

Answer 23

k^2 not h^2, right?

Answer 24

(y-k)^2=y^2-2yk+k^2
right

Answer 25

now combine them, (x-h)^2 +(y-k)^2 =? (expand form)

Answer 26

(x -h)^2 = x^2 -2xh +h^2+(y-k)^2=y^2-2yk+k^2

Answer 27

yeah!!! now compare it with yours, what they are.

Answer 28

x^2 -2xh +h^2+y^2-2yk+k^2

Answer 29

sorta not really, like I see that they have some similarities

Answer 30

ok