I need to find unit normal and tangent vectors for an ellipse with major axis ($\displaystyle x$) of length $\displaystyle a$ and minor axis ($\displaystyle y$) of length $\displaystyle b$.

My initial guesses are

$\displaystyle \hat{N}=b\cos{\theta}\hat{i}+a\sin{\theta}\hat{j}$

and

$\displaystyle \hat{T}=-a\sin{\theta}\hat{i}+b\cos{\theta}\hat{j}$

These are orthogonal, but lead to incorrect results later so I suspect they're wrong.

Anyone?