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  4. What is the slope of the normal at the point (at2, 2at) of the parabola y2 = 4ax ?

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Q. What is the slope of the normal at the point $(at^2, 2at)$ of the parabola $y^2 = 4ax$ ?

Application of Derivatives

Solution:

Equation of parabola is $y^{2} = 4ax $
$\Rightarrow 2y \frac{dy}{dx} = 4a $ (On differentiating w.r.t ‘x’ )
$\therefore \frac{dy}{dx} = \frac{2a}{y},$ [slope of tangent]
So, slope of normal $ = - \left(\frac{dx}{dy} \right)_{at^{2} , 2 at} $
$ = - \left(\frac{y}{2a}\right) = - \frac{2at}{2a} = - t $