Find the equations of the tangent and normal to the given curves at the indicated points:

y = x² at (0, 0)

It is given that equation of curve is y = x²

On differentiating with respect to x, we get

= 2x

Therefore, the slope of the tangent at (0, 0) is 0.

Then, the equation of the tangent is

y – 0 = 0(x – 0)

⇒ y = 0

Then, slope of normal at (0,0)

=

Now, equation of the normal at (0,0)

x = 0