Find the equation of the set of all points P(x,y) that is equidistant from (-3,0) and (3,-5).

Answer 1

they lie on the perpendicular bisector of the line between the two points.

That line has slope -5/6, so its perpendicular has slope 6/5

The midpoint of the line segment is (0,-5/2), so the line you want is

y + 5/2 = 6/5 (x-0)