Question

please help
one question
medal + fan


*note: i am not asking for an answer but i am asking for help and guidance. i will admit i am not sure how to do this but I'm still not asking for an answer just patience and guidance.*

Answer 1

(if i am gone its because i am helping someone but no worry i still will come here and work)

Answer 2

You can find the centre and radius by converting to the standard form
(x - a)^2 + ( y - b)^2 = r^2

where the centre is (a,b) and r = the radius.

Answer 3

you can do this by completing the square on the terms in x and the terms in y:

x^2 + 4x + y^2 - 6y= -4

(x + 2)^2 -4 + y^2 - 6y = -4

- thats completing the square on the terms in x.
You do the same thing with y^2 + 6x

Answer 4

to complete the square use the identity
x^2 + bx = (x +(b/2)^2 - (b/2)^2

Answer 5

move all the numbers to RHS of the '=' . this number will equal r^2

Answer 6

* error back 3 posts
that y^2 - 6y not y^2 + 6x

Answer 7

O.O I'm sorry, I'm a little confused. @cwrw238

Answer 8

@jdoe0001
@jim_thompson5910
@superdavesuper

Answer 9

What's the general equation for a circle? Do you have that in your notes?

Answer 10

Yes I do, please give me a sec to type it in.

Answer 11

ok take your time

Answer 12

(x–h)2 + (y–k)2 = r2, where (h, k) is the center and r is the radius.

Answer 13

I think you meant to write

(x-h)^2 + (y-k)^2 = r^2

right?

Answer 14

oh oops lol yeah forgot to put the "^"

Answer 15

ok so we have this to start with

x^2 + 4x + y^2 - 6y= -4

Answer 16

is that in the form (x-h)^2 + (y-k)^2 = r^2 ?

Answer 17

doesn't look like it.

Answer 18

correct, it is not in that form

Answer 19

so we have to transform it into that form

Answer 20

to do that we complete the square for the x and y terms

Answer 21

focus on just the x terms (either with an x or x^2 in them)

x^2 + 4x

is this a perfect square? if so, then what does it factor to? if not, then what is missing to make it a perfect square?

Answer 22

I think it is a perfect square?

Answer 23

what does x^2 + 4x factor to?

a perfect square is something in the form S^2 where S is some expression

example: x^2 is a perfect square, so is (y-10)^2, so is 225 (since 225 = 15^2)

Answer 24

so are you able to put x^2 + 4x into the form S^2 ?

Answer 25

@jim_thompson5910 im so sorry for asking for your help. i literally just went through my lesson again and there is a step-by-step on solving this, i am truly sorry. i will still give you a medal and i am already fanned to you. thanks so much.

Answer 26

that's ok. I'm glad you found the solution to it