8

Part of 1970 Canada National Olympiad

Problems(1)

Locus of midpoints

Source: Canada 1970, Problem 8

Consider all line segments of length 4 with one end-point on the line

y=x

and the other end-point on the line

y=2x

. Find the equation of the locus of the midpoints of these line segments.

parameterizationconicsellipsegeometry unsolvedgeometry