Find the equation
Question:

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

$y^{2}=4 x$ at $(1,2)$

Solution:

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

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

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

$\mathrm{m}$ (tangent) at $(1,2)=1$

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

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

$y-2=1(x-1)$

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

$y-2=-1(x-1)$