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Answer 1 · 2017-10-10T12:50:43

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

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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 $(4,4)$