The normal is a dotted line that is always perpendicular to the plane. In mathematical geometry, normal refers to a straight line on a plane perpendicular to the tangent of a curve at a certain point. Normal also applies to plane mirror reflection in physics.

For example:

distinguish

2y*y'=2p

y'=p/y

So for the point (x, y) on the parabola, the tangent slope is p/y.

Normal slope =-1/(p/y) =-y/p.

Slope of the normal at the point (p/2, p) =-p/p=- 1.

Normal equation: y-p=-(x-(p/2))

y=-x+(3/2)p

Extended data:

The equation of parabola y2=2px with focal slope k is y=k(x-p/2).

Domain: for parabola y 1=2px, p>0, the domain is x≥0, p.

Range: for parabola y 1=2px, range is r; for parabola x 1=2py, p>0, the range is y≥0, p.

If a surface has no tangent plane at a certain point, then there is no normal at that point. For example, the vertex and bottom edge of a cone have no normals, but the normals of the cone exist almost everywhere. Generally, a surface that satisfies Lipschitz continuity can be considered to have normals almost everywhere.

Baidu Encyclopedia-Normal