What is the equation of the normal to the par | vedclass

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(C) The equation of the normal to the parabola $y^2 = 4ax$ at the point $(at^2, 2at)$ is given by $y + tx = 2at + at^3$.Given the point $(\frac{a}{m^2

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$m^3y = 2am^2 - m^2x + a$

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(C) The equation of the normal to the parabola $y^2 = 4ax$ at the point $(at^2, 2at)$ is given by $y + tx = 2at + at^3$.Given the point $(\frac{a}{m^2}, \frac{2a}{m})$,we have $t = \frac{1}{m}$.Substituting $t = \frac{1}{m}$ into the normal equation:$y + (\frac{1}{m})x = 2a(\frac{1}{m}) + a(\frac{1}{m})^3$Multiply the entire equation by $m^3$:$m^3y + m^2x = 2am^2 + a$Rearranging the terms to match the form $m^3y = 2am^2 - m^2x + a$.

What is the equation of the normal to the parabola $y^2 = 4ax$ at the point $(\frac{a}{m^2}, \frac{2a}{m})$?

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