# JEE Main & Advanced Mathematics Applications of Derivatives Length of Perpendicular from Origin to the Tangent

## Length of Perpendicular from Origin to the Tangent

Category : JEE Main & Advanced

Length of perpendicular from origin $(0,\,0)$ to the tangent drawn at point $P({{x}_{1}},\,{{y}_{1}})$ of the curve $y=f(x)$ $p=\left| \,\frac{{{y}_{1}}-{{x}_{1}}{{\left( \frac{dy}{dx} \right)}_{({{x}_{1}},\,{{y}_{1}})}}}{\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}}\, \right|$ .

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