The maximum number of normals that can be dra | vedclass

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(D) The equation of a normal to the parabola $y^2 = 4ax$ with slope $m$ is given by $y = mx - 2am - am^3$.For a given point $(x_1, y_1)$ through which

Vedclass · Accepted Answer

$3$

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(D) The equation of a normal to the parabola $y^2 = 4ax$ with slope $m$ is given by $y = mx - 2am - am^3$.For a given point $(x_1, y_1)$ through which the normal passes,we have $y_1 = mx_1 - 2am - am^3$.Rearranging this,we get the cubic equation in $m$: $am^3 + (2a - x_1)m + y_1 = 0$.Since this is a cubic equation in $m$,it can have at most $3$ real roots.Therefore,a maximum of $3$ normals can be drawn from a point to a parabola.

The maximum number of normals that can be drawn from a point to a parabola is

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