# Thread: Prove that the intersection of tang. in OY from point P is equal to intersection ox.

1. ## Prove that the intersection of tang. in OY from point P is equal to intersection ox.

Hello guys,
Can anyone help me with this problem.

So I graphed the function.
And I used similar triangles.

So I did the normal from P to Ox, and normal from P to Y.

I did the similarity of the big triangle and both of the small triangle.

But I dont know how to proceed.

2. ## Re: Prove that the intersection of tang. in OY from point P is equal to intersection

Let the point of tangency be $\left(p,\dfrac{a}{p}\right)$

Tangent line at that point is ...

$y=-\dfrac{ax}{p^2}+\dfrac{2a}{p}$

Point B is $\left(0,\dfrac{2a}{p}\right)$

Point A is $\left(2p,0\right)$

Midpoint of AB is $\left(p,\dfrac{a}{p}\right)$

conclusion is ...

3. ## Re: Prove that the intersection of tang. in OY from point P is equal to intersection

Oh, got it.

Thank you very much.

4. ## Re: Prove that the intersection of tang. in OY from point P is equal to intersection

Your last question has been moved to a new thread. Multiple problems in the same thread tends toward confusion. In future start new problems with a new thread. Thank you.