Question

MEDAL!!!HELP!!! 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 (8 points)

Answer 1

Help???

Answer 2

start by grouping x and y terms separately

Answer 3

Oops the first one is x^2
And y2 is actually y^2

Answer 4

\[\large x^2 + 2x + y^2 + 4y = 19\]
\[\large (x^2 + 2x) + (y^2 + 4y) = 19\]

Answer 5

like that, eh ?

Answer 6

OK

Answer 7

So, now what do I do?

Answer 8

heard of the phrase `completing the square` before ?

Answer 9

No

Answer 10

Wait... yeah I did

Answer 11

good, next step is to complete the square for the stuff inside each parenthesis

Answer 12

So I add one to both sides

Answer 13

Then I factor the parentheses???

Answer 14

kindof...

Answer 15

Are you still on?

Answer 16

\[\large x^2 + 2x + y^2 + 4y = 19\]
\[\large (x^2 + 2x) + (y^2 + 4y) = 19\]
\[\large (x^2 + 2x + \color{red}{1^2}) + (y^2 + 4y +\color{red}{ 2^2}) = 19 + \color{Red}{1^2 + 2^2}\]

Answer 17

Hello?

Answer 18

we're almost done, knw how to complete the square ?

Answer 19

use below identity :
\(a^2 + 2ab + b^2 = (a+b)^2\)

Answer 20

I heard it but I forgot

Answer 21

What;s that mean?

Answer 22

\[\large (x^2 + 2x + \color{red}{1^2}) + (y^2 + 4y +\color{red}{ 2^2}) = 19 + \color{Red}{1^2 + 2^2} \]
\[\large (x+1)^2 + (y+2)^2 = 19 + 1 + 4 \]
\[\large (x+1)^2 + (y+2)^2 = 24 \]

Answer 23

compare that equation with the standard form of circle :
\[\large (x-h)^2 + (y-k)^2 = r^2\]

center = \(\large (h, k)\)
radius = \(\large r\)