Loser66
  • Loser66
any circle can be written in the form \(x^2 + y^2 + cx + dy +e =0\) Write equation of the circle passes through A (0,1) , B ( 1,3), C ( 2,5). Please, help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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imqwerty
  • imqwerty
hmm a length method will be to find the equation of AB and BC and then their normal the point where the normals intersect is the centre once we get the center we can find the radius and then we r done
Loser66
  • Loser66
Replace: for A: d + e =-1(1) for B: c + 3d +e = -10 (2) for C: 2c + 5d +e = -29 (3) If I multiple (2) by 2 and subtract (3) from it, I have d +e = 9 hence with (1) , we have no solution. But it is obviously wrong. However, I don't see what is wrong with the logic.
Loser66
  • Loser66
When solving it by matrix, I got c = -5, d= -2, e = 1. But I need know what is wrong with the logic above.

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More answers

Zarkon
  • Zarkon
isn't A, B and C colinear
amistre64
  • amistre64
A (0,1) , B ( 1,3), C ( 2,5) cx+dy+e=-(x^2+y^2) 0c+1d+1e=-1 1c+3d+1e=-10 2c+5d+1e=-29 by elimination ... -2c-6d-2e= 20 2c+5d+1e=-29 -------------- d+e = 9 rref{{0,1,1},{1,3,1},{2,5,1}} = 1,0,-2 0,1,1 0,0,0 we have a free .... radical? forget the term ... but the matrix is not independant d+e = 9 d+e = 1
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
you got a line there with slope two and y intercept one must be a magic circle
misty1212
  • misty1212
oh, what @Zarkon said
imqwerty
  • imqwerty
lol yes they r collinear xD so circle shuld not exist slope of AB= slope of BC cx
Loser66
  • Loser66
:) Shame on me.!! Thanks all .
amistre64
  • amistre64
if its a circle, then you are looking at it from the wrong angle :)
Loser66
  • Loser66
But I don't know why I put it on my calculator, it gives me the answer c = -5, d = -2, e =1. :(((
amistre64
  • amistre64
user error?
Loser66
  • Loser66
I put the numbers in 3 x 4 matrix and hit the rref, the result pops out like this. hehehe.... it is crazy like me.
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=rref{{1%2C3%2C1%2C-10}%2C{2%2C5%2C1%2C-29}%2C{0%2C1%2C1%2C-1}}
amistre64
  • amistre64
firefox likes to post broken links i spose
Loser66
  • Loser66
is it not that |dw:1446408277802:dw|
Loser66
  • Loser66
Why do you ignore the numbers from the right hand side?
amistre64
  • amistre64
|dw:1446408339152:dw|
Loser66
  • Loser66
yeah, you are right!! :)

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