Find the equation


Find the equation of the tangent and the normal to the following curves at the indicated points:

$y^{2}=4 a x$ at $\left(x_{1}, y_{1}\right)$


finding slope of the tangent by differentiating the curve

$2 y \frac{d y}{d x}=4 a$

$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{2 \mathrm{a}}{\mathrm{y}}$

$\mathrm{m}($ tangent $)$ at $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=\frac{2 \mathrm{a}}{\mathrm{y}_{1}}$

$m($ normal $)$ at $\left(x_{1}, y_{1}\right)=-\frac{y_{1}}{2 a}$c

equation of tangent is given by $y-y_{1}=m(\operatorname{tangent})\left(x-x_{1}\right)$

$y-y_{1}=\frac{2 a}{y_{1}}\left(x-x_{1}\right)$

equation of normal is given by $y-y_{1}=m($ normal $)\left(x-x_{1}\right)$

$y-y_{1}=-\frac{y_{1}}{2 a}\left(x-x_{1}\right)$

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