Hello Sunyata Originally Posted by

**Sunyata** How about when P and Q are the same points Grandad?

So - what about it? What is the point you are making?

It is meaningless to talk about the point of intersection of two tangents if the tangents are drawn at one and the same point. In the algebra, the point of intersection of the tangents at P and Q is found by solving the equation:

$\displaystyle (p-q)x=a(p^2-q^2)$$\displaystyle =a(p-q)(p+q)$

We can divide both sides by $\displaystyle (p-q)$ to get the solution:

$\displaystyle x=a(p+q)$

only if $\displaystyle p\ne q$; otherwise we should be dividing by zero - and that's not allowed!

Grandad