Let \[P\left( x\text{ },\text{ }y \right)\] be any point on the curve,
AB be the tangent to the given curve at P.
A/Q, P is the mid-point of AB
HENCE,
the coordinates of \[A\text{ }is\text{ }\left( 2x,\text{ }0 \right)\text{ }and\text{ }B\text{ }is\text{ }\left( 0,\text{ }2y \right).\]
Also,
The slope of the tangent AB
\[=\text{ }\left( 2y\text{ }\text{ }0 \right)/\text{ }\left( 0\text{ }\text{ }2x \right)\text{ }=\text{ }-y/x\]
And hence, required equation is \[xy\text{ }=\text{ }1\]