Question

Prove that the point (-1,6),(5,2),(7,0) and (-1,-4) are concyclic

Answer 1

Answer:

We can prove this by using standard equation of circle.

The standard equation of the of a circle x2+y2+dx+ey+f=0

Put points (1,0) ,(2,-7) ,(9,-6) in equations of circle, we get three equations respectively.

1+d+f=0 ,

2d-7e+f=-53 ,

9d-6e+f=-117

Now after solving these equations, we get d= -10, e= 6, f=9.

For the proof of the concyclicity, we have to form the standard equation and then we have to check whether the fourth point satisfy the standard equation or not if it will satisfy the equation then these points are concyclic