Let be on . For simplicity sake assume,Originally Posted bytotalnewbie

.

Now the tangent line to point is the derivative at that point. Thus, is the slope of the derivative. Now find the equation of the tangent.

The equation of line having slope and point is (by point slope formula is):

Now the x-intercept is when . Thus,

Thus,

Thus,

Thus, it intercepts the x-axis at .

This would imply that the base of the triangle must be

And its height to be . Thus, the area must be a constant for whatever value of .

Similarily it is true when . For one thing this hyperbola is symettric.

Q.E.D.