Question 21359: Write the equation of the circle through the points (-1,0), (2,1), (0,3).
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! EQN. OF A CIRCLE IS GIVEN BY
X^2+Y^2+2GX+2FY+C=0...IT IS PASSING THROUGH (-1,0),(2,1)AND (0,3)..SO SUBSTITUTING WE GET
1+0-2G+0+C=0...OR............-2G+C=-1.....................I
4+1+4G+2F+C=0....OR.........4G+2F+C=-5.....................II
0+9+0+6F+C=0......OR........6F+C=-9..........................III
II-I..........6G+2F=-4........................IV
III-I.........2G+6F=-8...........................V
V-3*IV........-16G=4....OR G=-1/4....SUBSTITUTING IN I WE GET 1/2+C=-1..OR.. C=-3/2....SUBSTITUTING IN III WE GET....6F-3/2=-9..OR.....
6F=-9+3/2=-15/2...OR.....F=-5/4
HENCE THE EQN.OF CIRCLE IS
X^2+Y^2-X/2-5Y/2-3/2=0....OR.....
2X^2+2Y^2-X-5Y-3=0
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