# Definition of the normal to the curve

Please refer to the following picture.

A tangent is a line that touches the curve at only one point.

A normal is a line perpendicular to the tangent. Is that the definition of a normal?

Or is the definition of a normal a line that is perpendicular to the tangent at the point where it touches the curve?

Because if the first definition is correct, then can't the line $N_2$ be a normal as well? We know $N_1$ is a normal. But what about $N_2$?

• A tangent is a line that touches the curve at only one point. This is a very awkward definition (and certainly doesn't agree with the most spread definition of a tangent). – gniourf_gniourf Dec 22 '16 at 12:10