So, what do we know?

1) We've a curve. y = f(x)

2) We've two lines. y = mx + b (Tangent) y = nx + c (Normal)

3) They all three intersect at the given arbitrary point (s,t): f(s) = m(s) + b = n(s) + c = t

4) Two slopes are equal at (x,y): f'(s) = m

5) Definition of Normal: m*n = -1

6) Intercepts: 0 = m(x) + b (Tangent) y = n(0) + c (Normal) ==> c = -b/m

There's a lot of information in there. Let's see if you get all the same information and what you can do with it.