what you do it complete the square for x's and y's
group x's and y's together
I mean group x with x and y with y
16x²-8x+16y²-32y=127
group
(16x²-8x)+(16y²-32y)=127
complete the squqare for each
first, factor out linear coefient of each
16(x²-1/2x)+16(y²-2y)=127
take 1/2 of each linear coefient then square it then add negative and positive inisde
(-1/2)/2=-1/4, (-1/4)²=1/16
-2/2=-1, (-1)²=1
16(x²-1/2x+1/16-1/16)+16(y²-2y+1-1)=127
factor perfect squares
16((x-1/4)²-1/16)+16((y-1)²-1)=127
expand
16(x-1/4)²-1+16(y-1)²-16=127
16(x-1/4)²+16(y-1)²-17=127
add 17 to both sides
16(x-1/4)²+16(y-1)²=144
divide both sides by 16
(x-1/4)²+(y-1)²=9
or
(x-1/4)²+(y-1)²=3²
das is equal of circle with center at (1/4,1) and radius of 3
