# JEE Main & Advanced Mathematics Applications of Derivatives Equation of the Tangent and Normal

## Equation of the Tangent and Normal

Category : JEE Main & Advanced

(1) Equation of the tangent : The equation of the tangent to the curve $f'(a)$ at a point $P({{x}_{1}},\,{{y}_{1}})$ is $y-{{y}_{1}}={{\left( \frac{dy}{dx} \right)}_{({{x}_{1}},\,{{y}_{1}})}}(x-{{x}_{1}})$.

(2) Equation of the normal :  The equation of the normal to the curve $y=f(x)$ at a point $P({{x}_{1}},\,{{y}_{1}})$ is $y-{{y}_{1}}=\frac{-1}{\left( \frac{dy}{dx} \right)_{({{x}_{1}},\,{{y}_{1}})}^{{}}}(x-{{x}_{1}})$

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