let $A$ be the point $(0, 4)$ in the $xy$-plane and let $B$ be the point $(2t, 0)$. Let $L$ be the midpoint of $AB$ and let the perpendicular bisector of $AB$ meets the $y$-axis at $M$. Let $N$ be the midpoint of $LM$. Find the locus of $N$ (as $t$ varies).
I was trying this question many times. I don't know where I have to start. I was thinking that this the locus of circle , because it moving around the midpoint $LM$. I don't know how to do this question.. If anybody help me I would very thankful to him.