Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x^2 + 2x + y^2 + 4y = 20

Answer 1

Please help :)

Answer 2

can you convert the equation to (x-h)^2+(y-k)^2= r^2 format?

Answer 3

also there is a direct formila which you can use but try with the first method first

Answer 4

No because the 2x is cofusing me

Answer 5

(a+b)^2 = a^2+b^2+2ab now we know a=x and b is a number. so what should be value of b to make 2ab=2x?

Answer 6

I have no idea I'm so confused

Answer 7

lol ok (x+1)^2 can you expand this?

Answer 8

simplify? expand? I'm so sorry I have no idea what im doing

Answer 9

expand same way i did for (a+b)^2

Answer 10

(x+1).(x+1)=?

Answer 11

x.(x+1)+1(x+1)

Answer 12

Nevermind thanks anyways I honestly don;t think I can do this

Answer 13

Nooo don't give up

Answer 14

(x+1)^2+(y+2)^2 can you expand this?

Answer 15

I dont understand how to expand it I literally cannot think at all

Answer 16

hmm you know how to simplify (x+1)^2 ?

Answer 17

x^2+2?

Answer 18

What I originally got was x^2+2x)+(y^2+4y)=20...

Answer 19

it is like muliplying (x+1)(x+1) which is x(x+1)+1(x+1)

Answer 20

x^2+x+x+1= x^2+2x+1

Answer 21

so if you remember this formula (a+b)^2 = a^2+b^2+2ab you will be good
does any of this make sense?

Answer 22

Sort of.

Answer 23

This is my last essay and then I'm done I'm mentally exausted

Answer 24

haha ok you can try expanding (y+2)^2 lets see else take rest and do it later!

Answer 25

I can't sadly. I have to turn it in tonight. So oh well

Answer 26

I did x^2+ax+y^2+by=c then added the variabes as a=2, b=4, and c=20. So x^2+2x+y^2+4y=20. But i didnt know how to finish or if thatwas right so i give up

Answer 27

hmm it is correct so you can use the formula
center = -a/2,-b/2

Answer 28

so -1, -2?

Answer 29

and radius is sqrt(c-a^2/4 - b^2/4)

Answer 30

yeah

Answer 31

but I will suggest to learn the other way as well, anyway gn :)

Answer 32

16/-12/4? how do you solve that?

Answer 33

sqrt(20-1-4)

Answer 34

2.44?

Answer 35

oh no 20-12-4

Answer 36

so 2?

Answer 37

where is 12 comming from?

Answer 38

\[x^2 + 2x + y^2 + 4y = 20\]right?

Answer 39

takes one step
what is half of 2 ?