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Question

Locus of the image of the point (2,3) in the line (2x3y+4)+k(x2y+3)=0,k ϵ R, is a

A
Straight line parallel to x-axis
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B
Straight line parallel to y-axis
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C
Circle of radius 2
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D
Circle of adius 3
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Solution

The correct option is C Circle of radius 2
Lines (2x3y+4)+k(x2y+3)=0 pass throught point of intersection of 2x3y+4=0 and x2y+3=0 which is A(1,2)

Let image of P (2,3) in any line throught A be Q(α,β).
AP=AQ(α1)2+(β2)2=(21)2+(32)2α2+β22α4β+3=0or x2+y22x4y+3=0,
which is a circle having radius,
r=1+43=2

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