anonymous
  • anonymous
Rewrite in standard form. Find the center and radius of the circle. (Equation below and medal goes to the best helper)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[2x ^{2} + 2y ^{2} - 8x + 10y + 2 = 0\]
anonymous
  • anonymous
I have no idea how to do this :(
anonymous
  • anonymous
center is (2,-5/2) radius is square root of 37 divided by 2

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anonymous
  • anonymous
first step is to divide by 2
anonymous
  • anonymous
\[x^2+y^2-4x+5y+1=0\]
anonymous
  • anonymous
can you guys draw this out ??
anonymous
  • anonymous
next step is to complete the square twice do you know how to complete the square?
anonymous
  • anonymous
complete the square ?? i dont believe so, i just started this lesson im a online student.
anonymous
  • anonymous
if you do not know how to compete the square, then you cannot do it
anonymous
  • anonymous
i can show you (maybe) it only takes a couple steps
anonymous
  • anonymous
ok maybe your using different terminology for something I do know~ and yea that would be helpful my lessons dont help much
anonymous
  • anonymous
ok so first off do you know what the goal is here?
anonymous
  • anonymous
to wright the equation in standard forum
anonymous
  • anonymous
find center and radius
anonymous
  • anonymous
right, which is \[(x-h)^2+(y-k)^2=r^2\] notice that \((x-h)^2\) and \(y-k)^2\) are "perfect squares" i.e. the square of something that is why you have to "complete the square" twice once for the \(x\) terms and once for the \(y\) terms
anonymous
  • anonymous
lets group them together first \[x^2-4x+y^2+5y=-1\]
anonymous
  • anonymous
oh thats what u meant never heard that term ~
anonymous
  • anonymous
so we have to fill in these blanks for \(h\) and \(k\) \[(x-h)^2+(y-k)^2=-1+something\]
anonymous
  • anonymous
what is half of 4?
anonymous
  • anonymous
2
anonymous
  • anonymous
and what is \(2^2\)?
anonymous
  • anonymous
4
anonymous
  • anonymous
so our start is \[(x-2)^2+(y-k)^2=-1+4=3\] now we repeat for the y term
anonymous
  • anonymous
what is half of 5?
anonymous
  • anonymous
2.5
anonymous
  • anonymous
yes, but don't use a decimal
anonymous
  • anonymous
so what do i use ? 2 ? 3?
anonymous
  • anonymous
no, a fraction
anonymous
  • anonymous
\[\frac{ 2 }{ 5 }\] ?
anonymous
  • anonymous
you got it upside down!!
anonymous
  • anonymous
oh soo \[\frac{ 5 }{ 2}\]
anonymous
  • anonymous
yeah and what is \((\frac{5}{2})^2\)?
anonymous
  • anonymous
mmm gosh multiplying fractions :( ummm is it ... \[\frac{ 25 }{ 2 }\]
anonymous
  • anonymous
no, you forgot to square the two
anonymous
  • anonymous
ohh so \[\frac{ 25 }{ 4 }\]
anonymous
  • anonymous
I always thought you left the bottom number alone
anonymous
  • anonymous
right so now we have \[(x-2)^2+(y+\frac{5}{2})^2=3+\frac{25}{4}\]
anonymous
  • anonymous
that is called "completing the square" you have two competed squares on the left almost done, last step is only to add on the right, then it is in standard form
anonymous
  • anonymous
you leave the bottom number alone if you are ADDING fractions with like denominators for example \[\frac{5}{2}=\frac{8}{2}=\frac{13}{2}\]
anonymous
  • anonymous
but if you are multiplying you just multiply \[\left(\frac{5}{2}\right)^2=\frac{5}{2}\times \frac{5}{2}=\frac{25}{4}\]
anonymous
  • anonymous
ohh so this will be \[\left( x - 2 \right)^{2} +\left( y +\frac{ 5 }{ 2 } \right)^{2} = \frac{ 25 }{ 4} 3\]
anonymous
  • anonymous
?
anonymous
  • anonymous
what the heck kind of number is \(\frac{ 25 }{ 4} 3\)?? never seen a number that looked like that before
anonymous
  • anonymous
you gotta add !
anonymous
  • anonymous
well I thought i was adding I guess not ! ~ -.-
anonymous
  • anonymous
the way you wrote it, it looks like some sort of multiplication not sure in any case you get a fraction when you add
anonymous
  • anonymous
I added the 3 to the 25/4 at the end ~
anonymous
  • anonymous
\[3+\frac{25}{4}=\frac{3\times 4+25}{4}=\frac{37}{4}\]
anonymous
  • anonymous
oh I just added it as an whole number .. nvm alright soo i add that to the end and its the answer ?
anonymous
  • anonymous
ok well what about center and radius ?
anonymous
  • anonymous
\[(x-2)^2+(y+\frac{5}{2})^2=\frac{37}{4}\] is standard from you read the center and radius from that form
anonymous
  • anonymous
the center is \[(2,-\frac{5}{2})\] and the radius is \[\frac{\sqrt{37}}{2}\]
anonymous
  • anonymous
ohhhh ~~~ how so they where already in the equation ?

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