# Finding a Tangent Line to a Parabola

Finding a Tangent Line to a Parabola

There is a neat method for finding tangent lines to a parabola that does not involve calculus. In this problem, for example, to find the line tangent to at (1, -2) we can simultaneously solve and and set the discriminant equal to zero, which means that we want only one solution to the system (i.e., we want only one point of intersection).

y=x-3

2

y=x-3

2

y+2=m(x-1)