Hello UltraGirlI assume that you know how to use the parametric equations of the rectangular hyperbola:From these we get:

So the equation of the tangent at is:

i.e.

The intercepts of this line with the coordinate axes are and . And if the length of this line segment is , then:

Thus we have found four values of , which give the four required points when substituted into the parametric co-ordinates .

Grandad