A curve is given parametrically by

Find the equation of the normal to the curve at the point with parameter .

Find those points on the curve at which the normal is also normal to the curve at another point.

my attempt:

Gradient

normal

equation

The answer is:

So I got the RHS correct, but where on the LHS is wrong?

And for finding the points where the normal there is normal at another point, I don't know where to start.

Thanks for any help