Circles

If the line 2x-y+1=0 touches a circle at the point (2,5) and the centre of the circle lies on the line x+y-9=0, find the equation of the circle.

1 Answers

1133

Sourish Ghosh ·2013-02-21 08:59:48

The eqn will be
(x-2)² + (y-5)² + Î»(2x-y+1) = 0 , where Î» is any constant.

Centre of the circle is, ( 2-Î», 5+Î»2 )

The above co-ordinate will satisfy x+y-9=0. On solving we get Î» = -4.
Substitute this value and get the eqn.

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