# How you would find the equation of a line normal to a curve?

Apr 4, 2018

Use the derivative at that point.

#### Explanation:

Let the point be $\left({x}_{1} , {y}_{1}\right)$, of the function $y = f \left(x\right)$.

Let the slope of tangent at $\left({x}_{1} , {y}_{1}\right)$ be $m$.
Then $m = \frac{\mathrm{dy}}{\mathrm{dx}}$ at $\left({x}_{1} , {y}_{1}\right)$.

Then the slope of normal is $- \frac{1}{m}$.

Hence the equation of the normal is

$y - {y}_{1} = - \frac{1}{\frac{\mathrm{dy}}{\mathrm{dx}}} \left(x - {x}_{1}\right)$