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Answer 1 · 2017-10-10T12:50:43

The locus consists of two single points # (0,0)# and #(4,4)#

Steve M

The locus of points that is equidistant from, #(0,3)# and #(3,0)# is the line:

# L: \ \ \ \ y =x #

The locus of points that is 4 units from the point #(4,0)#, is a circle of radius #4# centered on #(4,0)#:

# C: \ \ \ \ (x-4)^2+y^2=4^2 #

There are only two points that satisfy both criteria, which is the intersection of #L# and #C#, which we can find from the graph as being:

# (0,0)# and #(4,4)#