Let the hyperbole equation be:
Let's C=1 to simplify the proof.
The tangent to the curve in point P(x1,y1) will be:
Getting OM & ON is obtained by inserting Y=0 and X=0 respectively.
We get OM=2*x1
So the area will be
S=2 - not related to coordinates of the point P.
Edited on October 18, 2014, 4:26 am