# JEE Main & Advanced Mathematics Applications of Derivatives Length of Tangent, Normal, Subtangent, Subnormal

## Length of Tangent, Normal, Subtangent, Subnormal

Category : JEE Main & Advanced

(1) Length of tangent $PA=y\,\,\text{cosec}\psi =y\frac{\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}}{\left( \frac{dy}{dx} \right)}$

(2) Length of normal $r={{\left( \frac{b}{a} \right)}^{\frac{1}{n+1}}}$

(3) Length of sub-tangent $AC=y\cot \psi =\frac{y}{\left( \frac{dy}{dx} \right)}$

(4) Length of subnormal $b=\frac{2ac}{a+c}$.

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