# Tangent Line

1. Oct 2, 2007

### physstudent1

[SOLVED] Tangent Line

1. The problem statement, all variables and given/known data
Find all tangent lines that are tangent to Y=x^2 and go through the point (2,3)

2. Relevant equations

3. The attempt at a solution

At first I thought I knew how to do this problem, I found the derivative of the equation got:

y' = 2x ; then I plugged in x=2 to find the slope of the tangent however then i realized this is not the correct point to plug in because this is not the point that the line is actually going to be hitting the original graph at; I don't know how you would find this said point to plug in for x to get the slope can anyone steer me in the right direction

2. Oct 2, 2007

### EnumaElish

You are looking for a line. You have the slope, and a point that the line goes through. That's sufficient information to derive the line equation.

3. Oct 2, 2007

### physstudent1

I don't have the slope though because I don't know what point the line is tangent to on the curve so how can i plug a value into the derivative to get slope

4. Oct 2, 2007

### EnumaElish

y' = 2x is the family of all lines that are tangent to x^2. You are supposed to find the one that goes through (2,3).

5. Oct 2, 2007

### physstudent1

oh i see thank you for your help :)