Consider a family of circles passing through two fixed points A(3,7) and B(6,5) .show that the chords in which the circle cuts the members of the family are cocurrent at a point .,The coorinate of this point is
: Let the circle be
It passes through A(3, 7) and B(6, 5)
-----------(1), (2)
Equation (2) and (1) gives
Hence from (1)
Hence the family of circles is
Common chord is given by
Above is of the form P + λ Q = 0, which passes through
the intersection of P = 0 and Q = 0
Solving 3x + 6y – 52 = 0 and 4x + 6y – 54 = 0
we get x = 2 and
∴ Required point is
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