JEE-Mains 2015 (19/30)

Geometry Level 3

Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0 \ , \ \ k \in \mathbb{R}$ is a :

circle of radius

\sqrt{2}

. straight line parallel to y-axis. circle of radius

\sqrt{3}

. straight line parallel to x-axis.

1 solution

Pushpa Sharma
May 19, 2017

The given line is a family of lines passing through the point of intersection of $2x-3y+4=0$ and $x-2y+3=0$ i.e. $P (1,2)$ . Let the co-ordinates of the image be $(h,k)$ . Distance of $P$ from $(2,3)$ is $\sqrt 2$ . So $(h,k)$ will also be at a distance of $\sqrt 2$ from $P$ . Therefore the locus is: $(h-1)^2 + (k-2)^2 = 2$ . Hence (B).

JEE-Mains 2015 (19/30)

1 solution

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