Question

Locus of a point P equidistant from two fixed points A and B is ____________

(a) an ellipse

(b) a line perpendicular to AB passing through the midpoint of AB

(c) a circle with AB as largest chord

(d) a parallel line of AB

This question was addressed to me in a national level competition.

The origin of the question is Loci of Points by Different Methods topic in division Loci of Points & Orthographic Projections of Engineering Drawing

Answer 1

Right option is (b) a line perpendicular to AB passing through the midpoint of AB

To explain: The line which makes equal distance from the two fixed points will definitely pass through the midpoint of line joining the two points and will definitely perpendicular to the line formed by joining the two points.