# Find all tangent lines through the origin

• February 10th 2013, 05:18 PM
Paze
Find all tangent lines through the origin
Find all tangent lines through the origin to the graph of $y=1+(x-1)^2$

I'm not even sure where to start! Help me MHF! :)
• February 10th 2013, 07:04 PM
chiro
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.
• February 10th 2013, 08:35 PM
ibdutt
Re: Find all tangent lines through the origin
• February 11th 2013, 01:24 PM
Paze
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?
• February 11th 2013, 02:18 PM
HallsofIvy
Re: Find all tangent lines through the origin
idbutt has pretty much given you the whole solution. What more do you want?
• February 11th 2013, 04:03 PM
Paze
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.
• February 11th 2013, 06:40 PM
ibdutt
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 Attachment 26968
• February 11th 2013, 09:02 PM
Paze
Re: Find all tangent lines through the origin
Ah, I get it. I was complicating your solution for myself. Thank you.