Thread: differential geometry locus question

what values of c is the locus of the function (x^2+x+y+3)y+z(x+y+3)+c a surface?

ok so my f=yx^2+yx+y^2+3y+zx+zy+3z+c..

i know that on a surface df cant equal zero..

my df=(2xy+y+z)dx+(x^2+x+2y+3)dy+(x+y+3)dz...

so how do i find c, if df cant equal zero?

but if x=y=z=0 df is 0, and it not 0 if c equals all reals except 0?

the thing im confused about if c is a constant? as soon as you differentiate it, it cancels?? coz c isnt even in df

umm i tried that df=0 if 2xy+y+z=0, x^2+x+2y+z+3=0, x+y+3=0?? but i solved for each x y and z and got really dumb answers, since its a quadratic..

ok please can someone help me, so far ive done

x+y+3=0=>y=-3-x
2x(-3-x)+(-3-x)+z=0=>z=2x^2+5x-3

then x^2+x+2(-3-x)+3+(2x^2+5x-3)=0

so x= -2/3 + and - root(22)/3????

and then its get worse, for the others.. i showed my lecturer and he said my approach was ok, but was making one small mistake, plz can someone show what im doing wrong?


srry that definitely wrong, forgot the z