# Find the equations of the tangent and normal to the given curves at the indicated points: $(iv) \: y = x^2\; at \;(0, 0)$

Toolbox:
• Equation of the tangent at $(x_1,y_1)$ where slope is $m$ is given by $y-y_1=m(x-x_1)$
• Equation of the normal at $(x_1,y_1)$ where slope is $m$ is given by $y-y_1=\large\frac{-1}{m}$$(x-x_1) Step 1: Given : y=x^2 Differentiating w.r.t x we get, \large\frac{dy}{dx}$$=2x$
Step 2:
The slope of the tangent at $(0,0)$ is $\large\frac{dy}{dx}_{(0,0)}=$$2(0) Therefore \large\frac{dy}{dx}$$=0$
Therefore the slope of the tangent at $(0,0)$ is $0$.
Hence the equation of the tangent is $(y-0)=0(x-0)$
$y=0$
Step 3:
Equation of the normal at $(0,0)$ is $x=0$