Equation of Normal Line

Slope of the Normal Line

The slope of the normal line to a curve at a point is the opposite of the inverse of the slope of the tangent, being mutually perpendicular lines.

Pendiente de la recta normal

That is to say, it is the opposite of the inverse of the derivative of the function at that point.

Normal Line to a Curve at a Point

The normal line to a curve at a point is one that passes through the point (a, f(a)) and whose slope is equal to the inverse of the opposite of f'(a).

Ecuación normal


Find the equation of the tangent and normal to the parabola y = x2 + x + 1 parallel to the bisector of the first quadrant.

P(a, b)

m = 1

f'(a) = 2a + 12a + 1 = 1 a = 0

P(0, 1)

Tangent line:

y − 1 = x y = x +1

Normal line:

m= 1P(0, 1)

y − 1 = −x y = −x + 1