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find equation and centre of the circle passing through the points(3,4),(3,2)&(1,4)
Asked by maramharinadh98 | 01 Nov, 2023, 09:45: AM
Expert Answer
Equation of Circle passing through (x,y) is
.......................... (1)If circle is passing through ( 3, 4 ) , then by substituting x = 3 and y = 4 , we get
6 g + 8 f + c = -25 .....................................(2)
If circle is passing through ( 3, 2 ) , then by substituting x = 3 and y = 2 , we get
6 g + 4 f + c = -13 .....................................(3)
If circle is passing through ( 1, 4 ) , then by substituting x = 1 and y = 4 , we get
2 g + 8 f + c = -17 .....................................(4)
Subtracting eqn.(3) from eqn.(2) , we get ,
4 f = -12 or f = -3
By substituting f = -3 in eqn.(2) and (4) , we get following simultaneous linear equations
6 g + c = -1
2 g + c = 7
By solving above equations , we get , g = - 2 and c = 11
Hence equation of circle from eqn.(1) is
Radius = 
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