1. Tangent on a curve

It's really hard for me to solve this problem. I would be gratefull if anybody could help me.

A tangent is drawn from point P on the curve y = 4 / x in the first quadrant. This limit together with the coordinate axes a triangle. Show that the area of this triangle is independent of the choice of P.

2. Originally Posted by hejmh
It's really hard for me to solve this problem. I would be gratefull if anybody could help me.

A tangent is drawn from point P on the curve y = 4 / x in the first quadrant. This limit together with the coordinate axes a triangle. Show that the area of this triangle is independent of the choice of P.
Start by setting $\displaystyle P=(x_1,y_1)$. Then differentiate y=4/x and work out the equation of the tangent.
Can you work out the general area of the triangle from this?