Question

Find the equation of the tangent and normal to the given curve at the given points $y=x^{2}at(0,0)$

Answer 1

The equation of the given curve is $y=x^2$

On differentiating w.r.t. x, we get $\frac{dy}{dx}=2x$

$\therefore$ Slope of tangent at (0,0) is ${\left(\frac{dy}{dx}\right)}_{(0,0)}=2\times 0=0$

Hence, the slope of the tangent at (0,0) having slope 0 is

$y-0=0(x-0)\Rightarrow y=0$

the slope of normal at (0,0) is $\frac{-1}{Slopeoftangentat(0,0)}=\frac{1}{0}$

Which is not defined.

Therefore, the equation of the normal at (x_0,y_0)=(0,0) is given by

$x=x_0=0$