JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 79

Every line of the family passes through the intersection of $2x-3y+4=0$ and $x-2y+3=0$, which is (1, 2). Reflection keeps the distance from (1, 2): $\sqrt{1+1}=\sqrt2$.

So the image lies on a circle of radius $\sqrt2$ about (1, 2).