What is the equation of this circle in standard form?
(x − 5.5)squared + (y − 4)squared = 7
(x + 5.5)squared + (y + 4)squared = 3.5
(x − 5.5)squared + (y − 4)squared = 3.5
(x + 5.5)squared + (y + 4)squared = 12.25
(x − 5.5)squared + (y − 4)squared = 12.25

- anonymous

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- anonymous

|dw:1436206108326:dw|

- anonymous

Is the center (2,4) and the point on the circle (9,4)?

- anonymous

no, (2,4) is also a point on the circle

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## More answers

- anonymous

the center doesn't have any coordinates

- anonymous

Ok, that makes more sense. So |dw:1436206427235:dw|

- anonymous

correct

- anonymous

So the diameter would be 7, right?

- anonymous

im not sure

- anonymous

ohh wait yea, sorry i had a dumb moment

- anonymous

Well, you can always fall back on the distance formula \[\large d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]\[\large d=\sqrt{(9-2)^{2} + (4-4)^{2}}\]\[\large d=\sqrt{(7)^2}\]\[\large d=7\]

- anonymous

But anyways, the diameter is 7, that means that the center of the circle is halfway between the x's of (2,4) and (9,4) right? Can you figure out what it is?

- anonymous

3.5

- anonymous

?

- anonymous

@LegendarySadist hey sorry! something happened that it logged me out

- anonymous

Hey, I'm back. Openstudy update kicked me out too

- anonymous

i got a little worried there lol i thought u weren't going to log back in

- anonymous

Anyway, if we know the radius is 3.5, then just add 3.5 to 2 to get the x of the center point.

- anonymous

5.5

- anonymous

Right, and the y is the same as both points.

- anonymous

So now we have all the info we need. All that's left is to put it into standard form. \[\large (x-h)^{2}~+~(y-k)^{2}=r^{2}\]
\[\large (h,k)~=~Center~coordinates~of~circle\]
\[\large r~=~radius\]

- anonymous

i hate this part like what is k supposed to be!?

- anonymous

\[\large (h,k) = (x,y)\\\large h=x \\\large k=y\]

- anonymous

ok give me a sec

- anonymous

wait but the y is what?

- anonymous

(h,k) is the (x,y) of the center coordinates. The k is the y of the center.

- anonymous

but what number does k stand for? lol im sorry

- anonymous

It's the same y as the other 2 points, so 4.

- anonymous

and x is 5.5?

- anonymous

Yep

- anonymous

i got 0

- anonymous

wait is it A?

- anonymous

Almost \[\large r^{2}\] not \[\large 2r\] So \[\large 3.5^{2}\]

- anonymous

so it's either D or E

- anonymous

is it E?

- anonymous

Yes, it would be E.

- anonymous

thank you sooo much!!!

- anonymous

\[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

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