How to Find Tangent Lines to Y=x^2 Passing Through (2,3) [SOLVED] Tangent Line

[physstudent1]

[SOLVED] Tangent Line

Homework Statement

Find all tangent lines that are tangent to Y=x^2 and go through the point (2,3)

Homework Equations

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

 

[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.

 

[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

 

[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).

 

[physstudent1]

oh i see thank you for your help :)