Question

Which is an equation of a circle with center (-10, 6) and radius 8?

Answer 1

The (vertex form of the) equation of a circle is:
\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{h}} )^2+ (y-{\rm \color{blue}{k}} )^2 = {\rm \color{green}{r}} }\)

Where
\(\large\color{black}{ \displaystyle({\rm \color{red}{h}} ,~{\rm \color{blue}{k}} )}\) is the center of the circle.
AND, \(\large\color{black}{ \displaystyle {\rm \color{green}{r}} }\) is the radius of the circle.

Answer 2

im confused still this stumps me..

Answer 3

what did u get?

Answer 4

LETS GO BACKWARDS.

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

In general,

\(\large\color{black}{ \displaystyle({\rm \color{red}{h}} ,~{\rm \color{blue}{k}} )}\) is the center of the circle.
AND, \(\large\color{black}{ \displaystyle {\rm \color{green}{r}} }\) is the radius of the circle.

\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{h}} )^2+ (y-{\rm \color{blue}{k}} )^2 = {\rm \color{green}{r}} }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

In your case,

\(\large\color{black}{ \displaystyle({\rm \color{red}{h}} ,~{\rm \color{blue}{k}} )}\) is the center of the circle, is (IN YOUR CASE) \(\large\color{black}{ \displaystyle({\rm \color{red}{-10}} ,~{\rm \color{blue}{6}} )}\)
AND, \(\large\color{black}{ \displaystyle {\rm \color{green}{r}} }\) is the radius of the circle, is (IN YOUR CASE) \(\large\color{black}{ \displaystyle {\rm \color{green}{8}} }\)

So, how would you fill in the equation of the circle?

( Also remember that for any numbers "a" and "b" , ` a - - a = a + a `
For example, `14- -13 = 14+13 = 27 ` )

Answer 5

would you like some examples, of actual (not abstract) equations of the circle problems, similar to your's ?

Answer 6

honestly im so frustrated with this i would just like the anwser i appreciate you trying to get me to undertand

Answer 7

I am not going to give the answer, if you would like an example though, then I can give you a bunch

Answer 8

I wrote the equation incoirrectly, btw.
The left side in equation always has r^2 (not just r)

Answer 9

i appreciate you trying to get me to understand, ive been trying for the past 2 hours and ive gotta go to work now and this worksheet is due tommorow morning so thats why i really just needed the anwser.

Answer 10

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid red ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Which is an equation of a circle with center (5, 3) and radius 4?

\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{5}} )^2+ (y-{\rm \color{blue}{3}} )^2 = {\rm \color{green}{4}^2} }\)
\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{5}} )^2+ (y-{\rm \color{blue}{3}} )^2 = 16 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid red ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Which is an equation of a circle with center (9, -1) and radius 2?

\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{9}} )^2+ (y-{\rm \color{blue}{(-1)}} )^2 = {\rm \color{green}{2}^2} }\)
\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{9}} )^2+ (y+{\rm \color{blue}{1}} )^2 = 4 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid red ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Which is an equation of a circle with center (-11, 4) and radius 13?

\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{(-11)}} )^2+ (y-{\rm \color{blue}{4}} )^2 = {\rm \color{green}{13}^2} }\)
\(\large\color{black}{ \displaystyle (x+{\rm \color{red}{11}} )^2+ (y-{\rm \color{blue}{4}} )^2 = 169 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, red ,border:2px solid red ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Which is an equation of a circle with center (-15, -2) and radius 6?

\(\large\color{black}{ \displaystyle (x-{\rm \color{red}{(-15)}} )^2+ (y-{\rm \color{blue}{(-2)}} )^2 = {\rm \color{green}{6}^2} }\)
\(\large\color{black}{ \displaystyle (x+{\rm \color{red}{15}} )^2+ (y+{\rm \color{blue}{2}} )^2 =36 }\)

Answer 11

these are some examples

Answer 12

still am not following you :(

Answer 13

I have given you all information and examples....

Answer 14

idk what to tell you then.
I am really not allowed to give out answer. If you want answers go to yahoo, here we "learn".

I can verify the answer, give you tips, examples etc... but doing your work and answers for you is not what I am authorized to do.

Answer 15

sorry

Answer 16

@scott895 there is really no math for you to do here
all you are doing is replacing variables
\[(x-h)^2+(y-k)^2=r^2 \\ \text{ where } (h,k) \text{ is center } \text{ and } r \text{ is radius }\]
you are given (h,k)=(-10,6) and r=8
So just make the proper substitutions in the equation given here.

Answer 17

give it your best shot
and we will check it

Answer 18

(x - 10)2 + (y + 6)2 = 8