anonymous
  • anonymous
Find the centre and the radius of circle X^2 + Y^2 - 4X+6Y =3
Precalculus
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Complete the square
anonymous
  • anonymous
\[x ^{2}+y ^{2}-4x+6y=3\]
anonymous
  • anonymous
Okay, so if you have \(y^2+6y\), then how do you complete the square?

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anonymous
  • anonymous
\[ (y+c)^2 = y^2+2cy +c^2 \]
anonymous
  • anonymous
if \(2c=6\) then \(c = 3\) and \(c^2=9\)
anonymous
  • anonymous
This means that\[ (y+3)^2 = y^2+6y+9 \]
anonymous
  • anonymous
Or in other words: \[ y^2+6y = (y+3)^2-9 \]This is how you complete the square.
anonymous
  • anonymous
\[ x ^{2}+y ^{2}-4x+6y=3 \]Is the same as \[ x ^{2}-4x+(y+3)^2-9=3 \]
anonymous
  • anonymous
Now you need to complete the square for \(x^2-4x\).
anonymous
  • anonymous
ok let me see
anonymous
  • anonymous
i got it thank you very much, it's been a while since i touched any question with circles, needed to brush up.
anonymous
  • anonymous
r=4, C(2, -3)

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