Question

Given `y=3x^2 - 2`, why/how is `x= sqrt(3)*t` and `y = t^2 -2` the parametric equations?

Answer 1

Given `y=3x^2-2`

Lets use parametrization given by

`x=t`

Then `y=3t^2-2` is the expresion given by this paramerization

In order to remove 3 from this expresion we can use instead

`x=t/sqrt3` in this case

`y=3(t/sqrt3)^2-2=t^2-2`

The parametrization given above result `x=sqrt3t` then

`y=9t^2-2`

So I think there is a mistake in parametrization of `x` in asked question. Hope this helps