Confusion regarding usage of 'a and b' in an ellipse

Question

In an ellipse I understand that the terms $a$ and $b$ are used to refer to the lengths of semi major and semi minor axes respectively. In my textbook there are different formulae for each of the cases; when $a>b$ and vice versa. However my teacher has said that it is okay to always take the (semi) length of axis along $x$-axis (I am talking about standard ellipses) as $a$ and correspondingly along $y$ as $b$. Which convention should I follow?