This Demonstration shows that all tangents on a one-parameter family of functions at a fixed go through some fixed point. In particular, it is true for parabolas .

All tangents on the graph of the general solution of an ordinary linear differential equation of the first order at a fixed have common point or are parallel. The general solution has form .

Reference

[1] V. I. Smirnoff, Lectures in Higher Mathematics (in Russian), Vol. II, Moscow: Nauka Publishers, 1967 p. 25.