>>11842279>>11843823Give that person back their money, seriously. The normal equation of a circle doesn't have a term in it, it has a term in it. It looks like . It's also literally the Pythagorean Theorem, which you should 200% realize if you're "half way through a math degree". Any actual understanding of basic trigonometry should make you realize this.
The reason why your example is shifted up 1 and centered at (0, 1) is because the equation in your example is only true on the same coordinates when y is shifted up 1, thus cancelling out the -1 (just like
>>11842396 said) and essentially being the same as the default equation for a circle.
Again, give that person back your money. Seriously.