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.