Problem 106E

106. A tangent line is drawn to the hyperbola $x y=c$ at a point $P$.

(a) Show that the midpoint of the line segment cut from this tangent line by the coordinate axes is $P$.

(b) Show that the triangle formed by the tangent line and the coordinate axes always has the same area, no matter where $P$ is located on the hyperbola.

Step-by-Step Solution