# 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.

**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). **

Find the equation of the tangent and normal to the parabola y = x^{2} + 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

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