Hello cheet0faceThere are no hard and fast rules about doing it this way round, but the equation you mention is a fairly standard one - it's a hyperbola, and a variation on the simpler version:

except that its centre has been moved from the origin to .

We use trig functions to write equations like this in parametric form. In this case we can use the fact that , by writing:

and

You'll see that if you eliminate between these two equations you get:

and

So, using the above trig identity:

Grandad