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

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regard

  • 17
What are you looking for?