# Normal to a Curve

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The normal to the curve is the line perpendicular (at right angles) to the tangent to the curve at that point. Its equation can be found out by the point-slope form as the tangent's point of contact and slope will be known.

If a line with slope 1 is tangent to a curve at the point $(1,1),$ find the equation of the normal at the curve at that point.

The slope of the normal is $-1.$ $($For perpendicular lines, the product of slopes is $-1.)$ We know that $(1,1)$ lies on it. Thus the equation is $y=mx+c$, where $m$ is $-1.$ Satisfy $(1,1)$ in the equation: $1=-1+c \implies c=2.$ Thus the equation of the normal to the curve at that point is $y=-x+2,$ or $x+y=2.\ _\square$

**Cite as:**Normal to a Curve.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/normal-to-a-curve/