Find the equation


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

$x y=c^{2}$ at $(c t, c / t)$


finding slope of the tangent by differentiating the curve


$m($ tangent $)$ at $\left(c t, \frac{c}{t}\right)=-\frac{1}{t^{2}}$

normal is perpendicular to tangent so, $m_{1} m_{2}=-1$

$\mathrm{m}$ (normal) at $\left(\mathrm{ct}, \frac{\mathrm{c}}{\mathrm{t}}\right)=\mathrm{t}^{2}$

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

$y-\frac{c}{t}=-\frac{1}{t^{2}}(x-c t)$

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

$y-\frac{c}{t}=t^{2}(x-c t)$

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