Question

Find the center and the radius of each circle. Graph each circle. Describe the translation from center (0, 0).
(x + 7)^2 + (y + 3)^2 = 49

I found the center just need help on radius

Answer 1

Circles take the form
\[\Large (x-h)^2 + (y-k)^2= r^2\]
Where the center is (h,k) and the radius is r ^_^

Follow the pattern :D

Answer 2

(x-(-7)^2+ (y-(-3)^2

Answer 3

That's good, so you know how to get the center, no problem ^^

There's just one little thing, and that's the radius. In your particular equation, which value corresponds to \(\large r^2\) ?

Answer 4

I have no idea..

Answer 5

Let me just lay it down for you, for your convenience ^^
\[\Large (x - \color{green}h)^2 + (y-\color{red}k)^2 = \color{blue}r^2\]\[\Large (x\color{green}{+7})^2 + (y\color{red}{+3})^2 = \color{blue}{49}\]

better? :D

Answer 6

So... *now* do you see which value corresponds to \(\large r^2\) ?

It's staring you right in the face.... ;)

Answer 7

49?

Answer 8

Yup. And BE CAREFUL, that's not the radius, that's the SQUARE of the radius.

Given that, what's the radius r, finally? :D

Answer 9

7? 24.5?

Answer 10

Which does your heart tell you? ;)

Remember... 49 is the square of the radius... the squaaare of the raaaadius (this works much better in a ghostly spooky voice)

Answer 11

7? Hahaha I dont know. I am drawing a blank.!

Answer 12

Trust your heart, Texas Girl (please feel free to tell me how you prefer to be called lol)

It can't be 24.5, that's way off, if you square 24.5, you get 600.25... which is so not 49 :D

\(\large 7^2\) on the other hand,is exactly 49.

So, are your heart and mind at ease now? ^^

Answer 13

Yes! Thank you so much!!

Answer 14

Good. My work here is done...

[Kurt walks off into the sunset]

Answer 15

I assume, now that you know the radius and the center, graphing this blasted circle would be a no-brainer? :D

Answer 16

Yes. Thanks a lot!

Answer 17

Okay. Have fun :D