Question
Locus the image of the point (2,3) in the line (2x - 3y +4) + k (x-2y+3) = 0, k ε R is a
-
straight line parallel to X - axis
-
a straight line parallel to Y- axis
-
circle of radius
-
circle of radius
Solution
C.
circle of radius
(2x-3y +4) +k (x-2y+3) = 0 is family of lines passing through (1,2). By congruency of triangles, we can prove that mirror image (h,k) and the point (2,3) will be equidistant from (1,2).
Therefore, Locus of (h,k) is PR = PQ
⇒ (h-1)2 + (k-2)2 = (2-1)2 + (3-2)2
(x-1)2 + (y-2)2 = 2
Locus is a circle of radius = 
