anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1436206108326:dw|
anonymous
  • anonymous
Is the center (2,4) and the point on the circle (9,4)?
anonymous
  • anonymous
no, (2,4) is also a point on the circle

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anonymous
  • anonymous
the center doesn't have any coordinates
anonymous
  • anonymous
Ok, that makes more sense. So |dw:1436206427235:dw|
anonymous
  • anonymous
correct
anonymous
  • anonymous
So the diameter would be 7, right?
anonymous
  • anonymous
im not sure
anonymous
  • anonymous
ohh wait yea, sorry i had a dumb moment
anonymous
  • 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
  • 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
  • anonymous
3.5
anonymous
  • anonymous
?
anonymous
  • anonymous
@LegendarySadist hey sorry! something happened that it logged me out
anonymous
  • anonymous
Hey, I'm back. Openstudy update kicked me out too
anonymous
  • anonymous
i got a little worried there lol i thought u weren't going to log back in
anonymous
  • 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
  • anonymous
5.5
anonymous
  • anonymous
Right, and the y is the same as both points.
anonymous
  • 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
  • anonymous
i hate this part like what is k supposed to be!?
anonymous
  • anonymous
\[\large (h,k) = (x,y)\\\large h=x \\\large k=y\]
anonymous
  • anonymous
ok give me a sec
anonymous
  • anonymous
wait but the y is what?
anonymous
  • anonymous
(h,k) is the (x,y) of the center coordinates. The k is the y of the center.
anonymous
  • anonymous
but what number does k stand for? lol im sorry
anonymous
  • anonymous
It's the same y as the other 2 points, so 4.
anonymous
  • anonymous
and x is 5.5?
anonymous
  • anonymous
Yep
anonymous
  • anonymous
i got 0
anonymous
  • anonymous
wait is it A?
anonymous
  • anonymous
Almost \[\large r^{2}\] not \[\large 2r\] So \[\large 3.5^{2}\]
anonymous
  • anonymous
so it's either D or E
anonymous
  • anonymous
is it E?
anonymous
  • anonymous
Yes, it would be E.
anonymous
  • anonymous
thank you sooo much!!!
anonymous
  • 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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