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 3 years ago
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.
 3 years ago
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.

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GT
 3 years ago
Best ResponseYou've already chosen the best response.0What are the points of the centers of the circles you have?

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1Do you know how to find the centres of the circles? Circle one is (2,3) I believe

kcbrosell
 3 years ago
Best ResponseYou've already chosen the best response.0The ? I asked is the only thing on the paper so I dont know what the points are

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1Oh, you said you had an answer. Would you like me to show you how to find the centres of the circles?

kcbrosell
 3 years ago
Best ResponseYou've already chosen the best response.0Yes I would, I came up with Neither

MrYantho
 3 years ago
Best ResponseYou've already chosen the best response.1You 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 \[(x ^{2}4x+44)+(y ^{2}+6y+99)+4=0\] \[(x ^{2}4x+4)4+(y ^{2}+6y+9)9+4=0\] simplify \[(x ^{2}4x+4)+(y ^{2}+6y+9)9=0\] Factor our x and y terms \[(x2)^{2}+(y+3)^{2}=9\] this means the centre of the circle is (2,3)
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