Sounds like the start of a simultaneous equations question!

A few more obscure ones.

I tried a few things before factoring the LHS and bisecting the asymptotes - I knew I was on the right lines because the numbers all worked so nicely! Well constructed :) how would you go about rotating if you don't already know the angle? I thought of trying it but couldn't see how.

I've used the 'any 4 points... parallelogram ' before - nice vectors proof. Never thought to do this though! Thanks