Find the equation

Question:

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

$y=x^{2}$ at $(0,0)$

Solution:

finding the slope of the tangent by differentiating the curve

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

$\mathrm{m}($ tangent $)$ at $(\mathrm{x}=0)=0$

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

$\mathrm{m}$ (normal) at $(\mathrm{x}=0)=\frac{1}{0}$

We can see that the slope of normal is not defined

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

$y=0$

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

$x=0$

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