Tangent Line and Natural Logaithmic Function?

Question

Let L be the tangent line to f(x)=lnx at the point (1,0)
a. find the equation of the line, L:
b. Let b be the y intercept of the line L: What is the distance between b and )????

2. Now, let T be the tangent line to f(x)=lnx at point (a, ln a) where a is a real number:

a. Find the equation of the line, T:

b. let b be the y intercept of the line T: What is the distance between b and ln a????

Any help would be great y'all. I have some answer but not to sure if they are right. Best answers will be given out. Thanks alot

Answer 1

Let´take the general case f(x)=ln x f´(x) = 1/x
At A(a,ln a) the tangent is
y-ln a= 1/a( x-a) .The y intercept is
(0,ln a-1) and its distance to (a,ln a) is
sqrt(a^2+1).
You can apply this formula to the first case with a=1