# Locus

Consider a rectangular hyperbola xy=c > 0.

There is a line passing through the origin where the point (s,t) have the perpendicular distance between 2 arbitrary points (a, c/a) and (b, c/b) on different quadrants the same.

Prove that ab+c=0

Consider 2 functions y=e^x and y=ln(x).

There is a line passing through the origin where the point (s,t) have the perpendicular distances between 2 arbitrary points (h, e^h) and (k, ln(k)) the same. By considering the midpoint of these 2 coordinates, prove that the line is y=x.

Consider 2 functions y=e^x and y=ln(x).

There is a line passing through the origin where the point (s,t) have the perpendicular distances between 2 arbitrary points (h, e^h) and (k, ln(k)) the same. By considering the midpoint of these 2 coordinates, prove that the line is y=x.

Hence, find the least perpendicular distance.

Consider a rectangular hyperbola xy=c > 0.

There is a line passing through the origin where the point (s,t) have the perpendicular distance between 2 arbitrary points (a, c/a) and (b, c/b) on different quadrants the same.

Prove that ab+c=0

Hence, explain why c must be non-zero.