Question

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

x2 + 2x + y2 + 4y = 20

@amistre64

Answer 1

i beleive you want to do thru a process called completing the square

Answer 2

you will also want to recall what the general equation of a circle looks like

Answer 3

yep, thats the general equation, and completing the square with that we have will transform it into that format

Answer 4

ok how do we do that

Answer 5

well it not that hard to do:

a complete square looks like:\[x^2 + bx + b^2/4\]

Answer 6

the reason it looks that way tends to be more useful than why it looks that way

Answer 7

(x+n)^2 = (x+n)(x+n) = x^2 +2n x + n^2

as such: n^2 = (2n/2)^2

Answer 8

since we want the (x+n) part of it, then when 2n = b n=b/2

Answer 9

hmmmm ;/ im trying to understand this

Answer 10

lots of practice helps :)

Answer 11

x2 + 2x + y2 + 4y = 20

(x2 + 2x) + (y2 + 4y) = 20

consider: x^2 + 2n x + n^2
= ax^2 + b x + c

2n = b, n = b/2, n^2 = b^2/4

Answer 12

yes, and so far i have attempted to describe up to step 3

Answer 13

complete the square is what i have always known it as

Answer 14

(x2 + 2x) + (y2 + 4y) = 20
+1 +4 +1+4
----------------------------
(x2 +2x+1) + (y2 +4y+4) = 25

Answer 15

(2/2)^2 = 1 and (4/2)^2 = 4

as i made mention of at the start

Answer 16

but the key is in knowning how to condense the sqaures into an (x+n)^2 format

n = b/2; so nx = 2/2 and ny = 4/2

Answer 17

ok..

Answer 18

i dont think ima learn how to do that now... so how do i find the radius and center ?

Answer 19

you have to do that in order to find them. if you cant learn that at the moment then you will have a rather difficult time finding them

Answer 20

one simple method would be to use the wolf, itll give you radius and center in its properties list

Answer 21

(x + 1)^2 + (y + 2)^2 = 25 ; yes

Answer 22

r^2 = 25 so r = sqrt(25) and you already stated you h and k parts effectively to me

Answer 23

so good ? haha

Answer 24

or is it 5 ..

Answer 25

yeah, its good :) just work the steps they gave you with the values required

r = sqrt(25) = 5

Answer 26

thats the radius ?

Answer 27

i hope so, otherwise im trying to figur eout what temperature to set the dishwasher at

Answer 28

cx lol ok thanks.

Answer 29

good luck :)