Let any point on the locus be P (x,y) so that your locus is all of these points.
Let your points (0,-1) be A and (0,9) be B
So the condition for your locus is PA + PB = 5
PA = rt[ (x - 0)² + (y- (-1))²] (distance formula)
= rt[x² + (y+1)²]
PB = rt[ (x - 0)² + (y - 9)²]
Sub these into PA +...