Locus of the image of the point (2,3) in the line (2x−3y+4)+k(x−2y+3)=0,kϵR, 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 (2x−3y+4)+k(x−2y+3)=0 pass throught point of intersection of 2x−3y+4=0 and x−2y+3=0 which is A(1,2)
Let image of P (2,3) in any line throught A be Q(α,β). ∴AP=AQ∴(α−1)2+(β−2)2=(2−1)2+(3−2)2∴α2+β2−2α−4β+3=0orx2+y2−2x−4y+3=0,
which is a circle having radius, r=√1+4−3=√2