What is the length of the subnormal at any po | vedclass

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(C) Given the equation of the parabola is $y^2 = 4ax$.Let $(x_1, y_1)$ be any point on the parabola.Differentiating $y^2 = 4ax$ with respect to $x$,we

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$2a$

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(C) Given the equation of the parabola is $y^2 = 4ax$.Let $(x_1, y_1)$ be any point on the parabola.Differentiating $y^2 = 4ax$ with respect to $x$,we get $2y \frac{dy}{dx} = 4a$,which implies $\frac{dy}{dx} = \frac{2a}{y}$.At the point $(x_1, y_1)$,the slope of the tangent is $m = \frac{dy}{dx} = \frac{2a}{y_1}$.The length of the subnormal is given by the formula $|y_1 \cdot \frac{dy}{dx}|$.Substituting the value of the slope,we get the length of the subnormal $= |y_1 \cdot \frac{2a}{y_1}| = 2a$.

What is the length of the subnormal at any point on the parabola $y^2 = 4ax$?

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