91Ó°ÊÓ

(a) Describe the locus of points 2 units from the y-axis and write an equation of this locus, (b) Describe the locus of points equidistant from the points \(\mathrm{P}_{1}(-4,2)\) and \(\mathrm{P}_{2}(-4,6)\) and write an equation for this locus. (c) Find the number of points which satisfy both conditions stated in (a) and (b) and give the coordinates of each point.

Prove that the locus of points equidistant from the ends of a given line segment is the perpendicular bisector of the line segment. Prove the converse of this statement.

(a) Write an equation of the locus of points whose distance from the origin is \(5 .\) (b) Determine whether the point \((-3,4)\) is on the locus.