Sketch graphs of: i. x^2 + y^2 = 1, ii. x^3 + y^3 = 1, iii. x^100 + y^100 = 1, iv. x^99 + y^99 = 1. Any generalisations?

i. A circle of radius 1 centred on the origin.ii. No longer restricted to -1 <= x,y <= 1, so its a quarter circle, then it goes off to infinity towards the asymptote x = -y.iii. Restricted to that range again, due to the even power. Sharper corners due to higher power. Looks like a square.iv. Similar to (ii) due to odd power, but due to higher power the turns are sharper.