Segment of the tangent to the curve xy=c2 at the points (x',y')which is contained between the co-ordinate axes, is bisected at the point:

[dydx](x',y')=−c2x'2=−y'x' ∴     Equation of tangent at (x',y') isy−y'=(−y'/x')(x−x')Which meets the co-ordinates axes at Aand B(say).Then A=(2x',0),B=(0,2y').Mid-point of AB=(x',y').