1st one involves general form of a circle. You divide the coefficients of the numbers with exponents of one by 2, and square em. Add these values to the other side of the equation. Then take the square root of this new value.
Your example, with 27x and 45y will have to be approximated to save time. 27/2 = (13.5)^2 = 180 and then 45/2 = 22.5^2 = 500. Add these values to the other side and you get 880ish. The closest square to that value is gonna be 29 or 30 depending on your way of approximating things.
On the other one, I dont know anything about sums of 4th power things. I'd skip or try to add them up. There's bound to be a shortcut here that I'm missing.
1) think about completing the square like Zack said... the right side would then have 200 + 180 + 500 = 880, that means r^2 = 880... multiply by pi = ~2700
2) I actually took 2005-2006 Dr. Numsen Oct 11 recently... and I assume you got this from it.. It's approximation so 1300+600+250 + 80 + 30 = ~2250
cube root = bit more than 13, square it to get an answer of 169 + some
