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Grade 12Algebra

(2,2) (3,-1) (3,-3) (0,0) is this a concyclic
Find out weather this is a concyclic or not
If it is not what number is equal to 0

Profile image of Alfred
7 Years agoGrade 12
Answers icon

1 Answer

Profile image of Rajat
7 Years ago
Equation of the circle passing through the first three coordinates be
x^2+y^2+2gx+2fy+c=0
Putting the coordinates in the above equation 
4g+4f+c=(-8) ....(1)
6g-2f+c=(-10)....(2)
6g-6f+c=(-18)....(3)
Eqn(1)-(2)
3f-g=1....(4)
Eqn(1)-(3)
5f-g=5....(5)
Eqn(5)-(4)
f=2
g=5
c=(-36)
Eqn of circle:
x^2+y^2+10x+4y-36=0
(0,0) doesn't satisfy the eqn. So coordinates are not concyclic.
Putting x=y
2x^2+14x-36=0
or, (x-2)(x+9)= 0
So, x= (-9) 
Therefore 0 must be replaced by (-9)
 

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