What is the maximum number of normals that ca | vedclass

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

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$3$

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(C) The equation of a normal to the parabola $y^2 = 4ax$ is given by $y = mx - 2am - am^3$.For a given point $(x_1, y_1)$ through which the normal passes,the equation becomes $y_1 = mx_1 - 2am - am^3$,which simplifies to $am^3 + (2a - x_1)m + y_1 = 0$.This is a cubic equation in $m$. Since a cubic equation can have at most $3$ real roots,there can be at most $3$ normals drawn from any point to the parabola.

What is the maximum number of normals that can be drawn from any interior point to a parabola?

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