Which point on the $y$-axis is equidistant from the points (6, 5) and (−4, 3)?

A point on the $y$-axis has the form (0, k). Equating squared distances: $36+(k-5{)}^2=16+(k-3{)}^2$, so $61-10k=25-6k$, giving $4k=36$ and $k=9$. Check: from (0, 9) both distances are √52.