Proving that a distance is always equal to 1
Hi guys, this is the second problem I have here in the math forums (and should be my last for a while, hopefully). (Speechless)
I am given a question that says I need to prove that the distance between a and c is always equal to one. The question also says that line "l" is the tangent line to the graph of the function y = e^x (of course, at the point where (a,b). C is when that line touches the x-axis.
The image below is what I made to try and make things clear for you.
So, I think I have an idea of how to prove it. Should I be trying to do something with the pythagorean theorem where the vertical line is the dotted line from point (a,b) to point (a) on the x axis and the other leg of the triangle is from a to c. The a - to - c leg is what I'm looking for to equal one.
x^2 + y^2 = c^2
Where x is a-to-c. Thus ...
x^2 = 1, so how do I prove this?