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 $N_2$?