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 = 19

Answer 1

@agent0smith

Answer 2

@mjdennis @.Sam. last question then finals :)

Answer 3

If you're back, take a look at this and I'll explain it further

Answer 4

one second let me read it

Answer 5

okay i read it

Answer 6

I'm stuck on that complex step

Answer 7

\[(x^2 + 2x+?) + (y^2 + 4y+?) = 19 \]
So, the half of 2 is 1, the squared of it is 1, as for 'y' the half of it is 2, squared it you get 4, add these to your RHS as well
\[(x^2 + 2x+1) + (y^2 + 4y+4) = 19 + 1+4 \]
\[(x^2 + 2x+1) + (y^2 + 4y+4) =24 \]

Answer 8

what what

Answer 9

wait what*

Answer 10

lol, right, from here you'll have to find the question mark and you'll take the 'Number' from 2x, and 4y. then, there's a method you'll need to make, take the half of 2x and 4y and square it, but without the x and y.
So, for x, half of 2 is 1, square of it is still 1. For you, half of 4 is 2, take the square of it is 4 again.
Then you'd put 1 and 4 accordingly
\[(x^2 + 2x+1) + (y^2 + 4y+4) = 19 + 1+4\]

Answer 11

ok where does the 1 and 4 go in the parenthesis?

Answer 12

I mean For 'y', not 'For you'

Answer 13

Put them as a number inside the parenthesis, with \((x^2+2x)\)

Answer 14

You'd get
\[(x^2 + 2x+1) + (y^2 + 4y+4) = 19 + 1+4\]

Answer 15

yes but after they're in there where do they go?

Answer 16

Let them be there because you'll need to factorize the two equations later

Answer 17

okay, I have that written down, now what?

Answer 18

Great now factorize x^2+2x+1

Answer 19

what do you mean by that?

Answer 20

Factorize into this I mean \[(x+1)^2\]

Answer 21

And you'll need to factorize y2+4y+4 as well

Answer 22

so \[(y+4)^2\]

Answer 23

?

Answer 24

Nope your values are off, if you expand it you won't get y2+4y+4

Answer 25

Try (y+2)^2

Answer 26

oh bc 2 is the square root of 4?

Answer 27

then I would square root the whole left side right? so it would look like
\[(x+1) + (y + 2) = 24\]

Answer 28

No just normal factorizing equation