The curve through (2,3) such that the segment of any tangent between the axes is bisected …

Question

The curve through $(2,3)$ such that the segment of any tangent between the axes is bisected by the point of contact is:

Accepted Answer

The intercept-bisection condition gives $\dfrac{dx}{x}=-\dfrac{dy}{y} \implies xy=c$. Through $(2,3)$: $c=6$, so $y=6/x$.

Solutions · 1