equation of circle passing through three points (0,1) (0,-1) (1,0)

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Please find below the solution to the asked query:

Consider the genral form of equaation of circle.   x2+y2+Cx+Dy+E=0Since the circle passes through the points 0,1, 0,-1, 1,0This gives,    02+12+C0+D1+E=0         1+D+E=0              D+E=-1        ......1and    02+-12+C0+D-1+E=0           1-D+E=0           -D+E=-1        ......2and    12+02+C1+D0+E=0         1+C+E=0           C+E=-1        ......3Add 1 and 2  to get,    D+E=-1  -D+E=-1      2E=-2      E=-1Put this value in 2    D-1=-1        D=-1+1        D=0Put E=-1 in 3  to get,     C-1=-1          C=-1+1           C=0  Therefore the required equation of circle is,     x2+y2+0x+0y-1=0     x2+y2-1=0          x2+y2=1

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