Question

x ^{2} +y ^{2} -2x +4y -4 =0 how do I find the center and radius of this equation?

Answer 1

Do you know how to complete the square?

Answer 2

If so, you would complete the square for x^2-2x
and do the same for y^2+4y

you want to get the equation in the form
(x-a)^2 + (y-b)^2 = r^2
(a,b) will be the center, and r the radius

Answer 3

@myko have you read the Code of Conduct?

Answer 4

what did myko do?

Answer 5

he thinks I willanswer your question

Answer 6

ahh

Answer 7

I just completed the square, and I got the correct center points but the wrong radius. I am not sure what I did wrong though..

Answer 8

show your work .

Answer 9

write it like this:
x^2-2x+1+y^2+4y+4-4-4-1=0

Answer 10

by the way @phi, maybe you can sugest me any good webpage on lebesgue mesure?

Answer 11

@myko I'm engineer not a mathematician

Answer 12

me too

Answer 13

\[(x ^{2}-2x) + (y ^{2} +4y) =4\] so then I divided -2 by 2, and then squared it which gave me 1 and then I divided 4 by 2 and squared it which then gave me 4. so now the equation looks like \[(x ^{2}-2x-1) + (y ^{2} +4y +2)=5\]
I then factored which gave me
\[(x-1) + (y-(-2) =5\]
so the center would be (1,-2) and the radius would be 5 but my book says that the radius is 3...

Answer 14

circle equation has a form :
\[(x-a)^2+(x-b)^2=c^2\]
where (a,b) would be the center and c the radius

Answer 15

that's why you need to compleate the squeres

Answer 16

you expression in parenthesis is not a square

Answer 17

remember when you square -1 you get +1
you want a +1 not a -1 in the x term

Answer 18

what do I do then?

Answer 19

x^2-2x +a = (x - sqrt(a))^2

Answer 20

what should be a=?

Answer 21

1?

Answer 22

right,
now do the same for y^2+4y +b=(y - sqrt(b))^2

Answer 23

4?

Answer 24

sry should be
(x + sqrt(a))^2
but 4 is right

Answer 25

now remmember to add/substract what you added to compleat the square so the expression doesn't change

Answer 26

so now i have (x+1) + (x+2) = 9

Answer 27

don't forget the exponents (the 2's)

Answer 28

sorry i meant (x+1) + (y+2) =9

Answer 29

You should have something like this:
(x^2-2x+1)+(y^2+4y+4)-4-4-1=0

Answer 30

which equals to: what you wrote, just with squares:
(x-1)^2 + (y+2)^2 =9

Answer 31

i have (x^2 - 2x +1) + (y^2 +4y +4), but not -4-4-1.. where did that come from?

Answer 32

never mind I see where it came from

Answer 33

if you add 1 to compleat the first square you also have to substract it, so the equation stays the same. Same for the 4 in the 2º square

Answer 34

so your radius would be?

Answer 35

3

Answer 36

right

Answer 37

but now my center is wrong.. i have (1,2) when it is supposed to be (1,-2)

Answer 38

it's right: (x^2-2x+1)+(y^2+4y+4)-4-4-1=0
equals to
(x-1)^2 + (y+2)^2 =9

Answer 39

so center (1,-2)

Answer 40

why is 2 negative?

Answer 41

remmeber what i wrote about how circle equation looks like, many comments ago...

Answer 42

yes..

Answer 43

so, that's why

Answer 44

(y+2)^2 is same as (y-(-2))^2

Answer 45

Oh okay. Thank you.

Answer 46

yw