anonymous
  • anonymous
Find an equation of the line containing the centers of the two circles x2 + y2 − 4x + 6y + 4 = 0 and x2 + y2 + 6x + 4y + 9 = 0 I have an answer for this 1 but I want to make sure I am right.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
What are the points of the centers of the circles you have?
anonymous
  • anonymous
Do you know how to find the centres of the circles? Circle one is (2,-3) I believe
anonymous
  • anonymous
The ? I asked is the only thing on the paper so I dont know what the points are

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anonymous
  • anonymous
Oh, you said you had an answer. Would you like me to show you how to find the centres of the circles?
anonymous
  • anonymous
Yes I would, I came up with Neither
anonymous
  • anonymous
You have to 'complete the square' for both the x terms and y terms. This is because you need the equation in standard form. \[x ^{2}+y ^{2}-4x+6y+4=0\] Gather \[x ^{2}-4x+y ^{2}+6y+4=0\] \[(x ^{2}-4x)+(y ^{2}+6y)+4=0\] Now comes the complete the square part \[(x ^{2}-4x+4-4)+(y ^{2}+6y+9-9)+4=0\] \[(x ^{2}-4x+4)-4+(y ^{2}+6y+9)-9+4=0\] simplify \[(x ^{2}-4x+4)+(y ^{2}+6y+9)-9=0\] Factor our x and y terms \[(x-2)^{2}+(y+3)^{2}=9\] this means the centre of the circle is (2,-3)

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