SOLUTION: find the center,radius and standard form in general and standard form if the given circle passes through (0,6) (4,-2) (9,3) (Use general form)

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Question 1086015: find the center,radius and standard form in general and standard form if the given circle passes through (0,6) (4,-2) (9,3) (Use general form)
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Use this general form of a circle,

.
.
(0,6)


1.
(4,-2)


2.
(9,3)


3.
Subtract 1 from 2,


4.
Subtract 1 from 3,


5.
Multiply 5 by -2 and add to 4,



Then,



and
finally,



So,



.
.
.
.

Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
find the center,radius and standard form in general and standard form if the given circle passes through (0,6) (4,-2) (9,3) (Use general form)
General for any circle:



We substitute each point and simplify:

Substituting (x,y) = (0,6)










Substituting (x,y) = (4,-2)









Substituting (x,y) = (9,3)









Solve the system of equations:




Solve that system by elimination, substitution, 
matrices, or a combination of those.

Get D=-8, E=-6, F=0





Place in standard form

Switch the two middle terms:



Multiply the coefficient of x by 1/2, get (1/2)(-8) = -4
Square -4, get (-4)˛ = +16
Add +16 after the second term, and add it to the right side.
Multiply the coefficient of y by 1/2, get (1/2)(-6) = -3
Square -3, get (-3)˛ = +9
Add +9 after the last term on the left, and add to right side.



Factor first three terms:  x˛-8x+16 = (x-4)(x-4) = (x-4)˛
Factor last three terms on left:  y˛-6x+9 = (y-3)(y-3) = (y-3)˛
Combine numbers on the right sides; 0+16+9 = 25



Compare to



Center = (h,k) = (4,3) , radius˛ = r˛ = 25, r=5



Edwin
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