The locus of the image of the point (2,3) in the line (2x-3y+4) + k(x-2y+3) = 0, k belongs to R is a :
(A) straight line parallel to x-axis    (B) straight line parallel to y-axis  
(C) circle of radius sq.rt.2                (D) circle of radius sq.rt.3   

Dear Student,
Please find below the solution to the asked query:

2x - 3y + 4 + kx - 2y + 3 = 0 is family of lines passing through 1, 2 Now look at the given figure:Taking triangle ABM and AB'M,AM=AM commonAMB=AMB'=90°BM=MB' Given AM is perpendicular bisector of BB'ABMAMB' SAShence,AB=AB' so,Let M is mid point of BB' and AM is  bisector of BB' where A is the point of intersection given lines x  2x  1 + y  2y  3 = 0M will lie on the above line:so,h+22  2h+22  1 + k+32  2k+32 3 = 0h-2h+k-1k-3=0h2-2h+k2-4k+3=0h-12+k-22=2replacing h by x and k by y.x-12+y-22=2correct option is c

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