# Thread: Find all tangent lines through the origin

1. ## Find all tangent lines through the origin

Find all tangent lines through the origin to the graph of $\displaystyle y=1+(x-1)^2$

I'm not even sure where to start! Help me MHF!

2. ## Re: Find all tangent lines through the origin

Hey Paze.

A line through the origin has the equation y = mx.

The tangent line at the point x has the form of m = f'(x) where f'(x) is the derivative function of f(x).

So you have to find all points of x where y = f'(x0)*x.

4. ## Re: Find all tangent lines through the origin

I'm sorry but I am still having a problem understanding this. I understand derivatives pretty well. Perhaps someone could graph this for me so I understand what is happening?

5. ## Re: Find all tangent lines through the origin

idbutt has pretty much given you the whole solution. What more do you want?

6. ## Re: Find all tangent lines through the origin

I guess I just don't understand the concept. Maybe this problem was misplaced in the course.

7. ## Re: Find all tangent lines through the origin

Please understand that the there will be infinitely many tangents to the curve but all will not be passing through the origin. It is for this reason that we consider point ( h,k) to ba point on the curve at which the tangent passes through the origin. OK

8. ## Re: Find all tangent lines through the origin

Ah, I get it. I was complicating your solution for myself. Thank you.

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### Tangent at origin

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