SOLUTION: Find the equation of the circle which passes through the points (-3,-4),(2,1), and (-6,5).

Algebra ->  Circles -> SOLUTION: Find the equation of the circle which passes through the points (-3,-4),(2,1), and (-6,5).      Log On


   

Question 1086893: Find the equation of the circle which passes through the points (-3,-4),(2,1), and (-6,5).
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general equation of a circle,
x%5E2%2By%5E2%2BAx%2BBy%2BC=0
So for (-3,-4),
%28-3%29%5E2%2B%28-4%29%5E2%2BA%28-3%29%2BB%28-4%29%2BC=0
9%2B16-3A-4B%2BC=0
1.3A%2B4B-C=25
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(2,1):
%282%29%5E2%2B%281%29%5E2%2BA%282%29%2BB%281%29%2BC=0
4%2B1%2B2A%2BB%2BC=0
2.2A%2BB%2BC=-5
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(-6,5),
%28-6%29%5E2%2B%285%29%5E2%2BA%28-6%29%2BB%285%29%2BC=0
36%2B25-6A%2B5B%2BC=0
3.6A-5B-C=61
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Eliminate C;
Add 1 and 2,
2A%2BB%2BC%2B3A%2B4B-C=-5%2B25
5A%2B5B=20
4.A%2BB=4
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Add 2 and 3,
2A%2BB%2BC%2B6A-5B-C=-5%2B61
8A-4B=56
5.2A-B=14
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Add 4 and 5 to eliminate B,
A%2BB%2B2A-B=14%2B4
3A=18
A=6
Now back substitute and find B and C to complete the circle.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the circle which passes through the points (-3,-4),(2,1), and (-6,5).
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I have an Excel sheet that does these:
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| x    y  x^2+y^2  1|
|-3   -4    25     1|
| 2    1     5     1| = 0
|-6    5    61     1|

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I enter the 3 points and get an equation for the circle.
Same for a parabola or hyperbola.